PLUS ONE CHAPTER‐2 ATOMC STRUCTURE
• •
The word ‘atom’ was derived from the Greek word ‘a-tomio’ which means ‘uncutable’or ‘non-divisible’. The atomic theory of matter was first proposed by Dalton called Dalton’s atomic theory.
Dalton’s atomic theory 1. Matter is made up of very small particles called atoms 2. Atoms are indivisible 3. Atoms of one element are same in physical and chemical properties 4. Atoms of different elements are different in physical and chemical properties 5. Atoms of each element has characteristic mass 6. Atoms take part in chemical reaction 7. Atoms of different element combines to form compounds. Merits 1. Can explain law of constant proportion, law of conservation of mass and law of multiple proportion. Demerits Failed to explain about isotops, atomic weight, inter atomic interactive forces and law of definite proportion for isotops. Discovery of sub atomic particles Discovery of electron(Cathode ray discharge Experiment) •
Cathode ray tube is a partially evacuated cylindrical glass tube fitted with two metallic electrodes connected to the oppositely charged poles of a high voltage source.
•
When the gas taken in the tube was subjected to very low pressure( approx. 10-4mm by a vacuum pump and high volt (10,000 V) is applied.
•
A stream of particles moving in the tube from cathode (Negative electrode) to anode (positive electrode). These stream of particles were known as cathode rays. It was discovered by Julius Plucker.
•
The flow of current from cathode to anode was further checked by making a hole in the anode and coating the tube behind anode with phosphorescent material zinc sulphide. The rays passing through anode, strike the zinc sulphide coating and make a bright spot on the coating.
Spandanam
Coaching for NEET Entrance Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive
1
www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE Properties of Cathode Rays • • • • • • • • • •
Moves in straight line Moves from cathode to anode Carry negatively charged particles Affected by electric and magnetic field Ionise the gas through which they pass Posses penetrating power ie., they can easily pass through thin foils of metals Affect photographic plate Can make fluorescence Carry material particles. e/m value does not depend upon the nature of gas and electrode.
Charge to Mass Ratio of Electrons (e/m) •
J.J. Thomson (1897) made a set-up of cathode ray tube and applied the electric and magnetic field perpendicular to each other as well as to the path of the electrons.
•
The amount of deviation of the particles from their path in the presence of electrical or magnetic field depends upon: (i)
(ii) (iii)
• • • •
the magnitude of the negative charge on the particle- greater the magnitude of the charge on the particle, greater is the interaction with the electric or magnetic field and thus greater is the deflection. the mass of the particle — lighter the particle, greater the deflection. the strength of the electrical or magnetic field — the deflection of electrons from its original path increases with the increase in the voltage across the electrodes, or the strength of the magnetic field.
when electric or magnetic field is applied then those rays deviate from their path. If only electric field is applied electrons deviate from their path and hit the cathode ray tube at point A. In an absence of both types of field electrons hit the screen at point B. When only magnetic field is applied electrons hit the cathode ray tube at pint C.
From the above experiment J.J. Thomson determine the charge to mass ratio of electrons.
.
e = Magnitude of charge on electron m = mass of electron E = strength of electric field B = strength of magnetic field r = radius of circular path on ZnS
Charge on the electron •
By oil drop experiment R.A. Millikan calculate the charge on electron.
•
Fine oil drops are allowed to pass through an ionized gas which is placed between two charged plate.
Spandanam
Coaching for NEET Entrance 2 Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive www.spandanamnews.blogspot.in
PLUS ONE CHAPTEER‐2 ATTOMC STRUCTURE •
Th he fall of th hese charge ed oil drop plets can be retarded d, acceleratted or mad de sta ationary de epending upon u the charge on the t dropletts and the polarity an nd strrength of th he voltage applied to o the plate..
•
carrefully mea asuring th he effects of electricall field stren ngth on th he motion of o oil dropllets, Miillikan con ncluded th hat the magnitude of electric cal charge,, q, on th he droplets s is alw ways an in ntegral multiple of th he electrica al charge, e, e that is, q = n e, where w n = 1, 1 2, 3... .
•
Th he charge 1.6022 x 10-19 C is the sm mallest me easurable quantity y of charge and is called unit nega ative charge 6022 x 10-19 C e = – 1.6 = 4.8 × 10-10 esu u
e Mass of electron • Ma ass of electtron = •
e 1.6022 × 10−19 C = 9.1 × 10−31 kg = 11 −1 e / m 1.76 × 10 Ckg
Th he mass 9.1 x 10-31 kg k (9.1 x 10 0-28 g) is ne early
1 th of that of hydrogeen atom. 1837
Discoverry of proto on (Anode rays discharge exp periment) • •
•
Goldsttein disco overed the e existence e of a new ty ype of rays s in the dis scharge tube. On pa assing the e electric discharge d at low pressu ure throug gh a discha arge tube having perforrated cath hode, he observed o a new type of rays streamin ng behind d the cathod de. These ray were named as s anode ra ays, or canal rays, con nsist of po ositively ch harged materrial particle es.
es of Anod de rays Propertie 1. Moves in straight liine om anode to t cathode e 2. Moves fro sitively cha arged partiicles 3. Carry pos b electric and magn netic field 4. Affected by e gas throu ugh which they pass s 5. Ionise the enetrating power p ie., they t can ea asily pass through t thiin foils of metals m 6. Posses pe otographic c plate 7. Affect pho ence 8. Can make fluoresce aterial partticles. 9. Carry ma u the nature n of gas g and ele ectrode. 10. e/m value depend upon
Coachin ng for NEE ET Entrance e 3 Coaching fthor NEET Entrance E th and 12 Special tu uition for 11 1 2 (Chemis stry and Bi iology). PH: 98952638 838 t and 12th (Chemistr S Special tuittion for 11th ry and Biolo ogy). PH: 9 9895263838 Sincere – Systematiic - Supporrtive www.spandanamnews.blogspot.in S Sincere – Sy ystematic - Supportiv ve
PLUS ONE CHAPTEER‐2 ATTOMC STRUCTURE amental particle of an a atom carrying on ne unit pos sitive charrge and A proton is a funda having mass m nearly y equal to the t mass of o an atom of hydrog gen. • • •
Ma ass of protton 1.672 2 x 10-27 kg g (1.672 x 10-24 g) Ch harge on the proton n is 1.6022 2 x 10-19 C. C 4 e/m ratio off proton is s 9.58 x 10 1 C/g
Discoverry of Neutrron Ne eutron was s discovere ed by Jame es Chadwic ck (1932), when he b bombarded d a thin foil of beryllium m ( 4 Be ) by y α-partic cles ( 2 He ), then ele ectrically neutral n pa articles ha aving a mass m 9
4
slightly grreater than n that of protons p werre emitted. He name ed those pa articles as neutrons. 9 4
•
1 Be + 42 He ⎯⎯ → 12 6 C + 0n
Ma ass of neuttron 1.674 4 x 10-27 kg g (1.674 x 10-24 g)
Name
Symbol
Charge e (C)
C Charge (esu u)
Relativ ve charge e
s (kg) Mass
Mass (amu) (
U Unit Mass M
Electron
e
–1.6022 x 10-19
– –4.8 x 10-100
-1
9.1 x 10-31
0..00054
0
Proton
p
+1.6022 x 10-19
+ +4.8x 10-10
+1
1.672 x 10-27
1.007 1
1
Neutron
n
0
0
0
1.674 x 10-27
1.008 1
1
ATOMIC MODELS 1. • • • • • •
J.J J.Thomson’s Atom Model This is the firstt atom mod del, known n as plum pudding model m (Raisin Pudding g model orr water melon model)) Accorrding to th his an atom m can be co onsidered as a spherre of radiu us 10-10m positiive charge and mass s is uniform mly distrib buted throu ugh out. Electrons The electrons e a uniform are mly embedd ded in it. As a whole w atom m is electriically neuttral. d sphere Positiively charged This atom model could no ot explain Specttra, Rutherford’s -ra ays scatterring experiiment.
Rutherfo ords -ray scattering g experim ment. (Gold d foil expe eriment) •
•
Rutherford allo owed a narrow bea am of -p particles, emittted from a radioactiv ve element, to bomba ard on a thin gold g foil (a approx.100 0nm). A mo ovable circ cular zinc c screen was w placed d at the back of the gold d foil.
Observattions • • •
Most of the -particles pa assed throu ugh the go old foil with hout devia ation. A few w -particle es were defflected through smalll angles. Very few -partticles retra aced their path. p Coaching for NEET Entrance E t and 12th (Chemistr S Special tuittion for 11th ry and Biolo ogy). PH: 9 9895263838 S Sincere – Sy ystematic - Supportiv ve
4
www.spandanamnews.blogspot.in
PLUS ONE CHAPTEER‐2 ATTOMC STRUCTURE Conclusiions Since e most of the -p particles passed p strraight throu ugh the foil f he su uggested that the atom conta ains large volume v of empty spa ace. Since e -particle es are pos sitively cha arged and d have consiiderable mass, m theirr deflection n through small angle es indicate es the pres sence of a heavy h posiitively charg ged mass at a the centtre of the atom. He called c it as nucleus. The bouncing back of the -parrticles indicates that the t nucleu us is highly y denser.
•
•
•
herford’s Atom A Model (Planettary atom m model) Ruth
2.
According g to this model m The most m of the e space in an atom is s empty. Every y atom has s an extrem mely smalll, positive charged c ce entral partt, known as nucleus.. The volume v off a nucleu us is very small com mpared to that of a an atom. ie. size of the 5 nucle eus is only y 1/10 of the t size of the atom. The magnitude m of the pos sitive charg ge of the nucleus n is different d fo or differentt atoms. The entire e mas ss of the atom a is co oncentrated d at the nucleus n an nd thereforre it is hig ghly dense er. The nucleus n is s surround ded by ne egative cha arged electtrons, whic ch balance e the posiitive charg ge of the nu ucleus so that the ato om as a wh hole is electtrically neu utral. The nucleus n is surrounded by electrons thatt move around the n nucleus witth a very high speed d in circula ar paths ca alled orbits. Electrons and the t nucleu us are held d together by b electros static forcess of attractionn.
• • •
• •
•
•
•
ons of Ruttherford’ Atom A Mod del Limitatio 1. It c could not explain e the e stability of an atom m Accord ding to Maxwell’s M of theory of electrromagnetic c radiation n, a charrged pa article, con ntinuously y accelera ating arou und an oppositely o charged particle will con ntinuously y emit ene ergy. Thus the electrron movin ng around the nucleu us must emit e rad diation and loose en nergy. As a result th he electron n would mo ove closer and close er to the e nucleus following a spiral pa ath and wo ould finally y fall into tthe nucleu us. Since su uch a collapse c do oes not tak ke place, attom is u att all unsta able. 2. It could c not explain e the e atomic sp pectrum of o hydrogen n 3. Fa ailed to exp plain discon ntinuous spectra, s electronic sttructure ettc. Order of siz O ze (radius) of o an atom m is 10-10m = 10-8cm O Order of siz ze (radius) o of nucleus is 10-15m = 10-13cm
n Atomic number • • •
It is i equal to the numb ber of proto ons presen nt in the nu ucleus of a an atom. Ato omic numb ber is designated by letter ‘z’. In the case of neutrall atom ato omic numb ber is equal to the n number off protons and eve en equal to o the number of elec ctrons in attom. Coaching for NEET Entrance E t and 12th (Chemistr S Special tuittion for 11th ry and Biolo ogy). PH: 9 9895263838 S Sincere – Sy ystematic - Supportiv ve
5
www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE Mass number • • • •
A
It is equal to the sum of the protons (p) and neutrons (n). ZX Mass number of an atom is designated by the letter ‘A’. Mass number (A) = No. of proton (p or z) + number of neutron (n) = No. of nucleons. Representation of atomic and mass Number
Isotopes • • •
These are the different atoms of the same element having same atomic number but different mass number. isotopes have same number of protons but different number of neutrons. 1 2 3 35 37 Eg. (i) (ii) 1H , 1H , 1H 17Cl , 17Cl
Isobars • These are the atoms of the different elements having same mass number but different atomic number. 40 and 40 14 and N14 • Eg. (i) (ii) 19K 20Ca 6C 7 Isotones • The atoms with same number of neutrons but different number of protons (atomic number) are called isotones. 39 and 40 23 and 24 • Eg. (i) (ii) 19K 20Ca 11Na 12Mg Isosters • The species having same number of atoms and same number of electrons • Eg. CO2 and N2O Isodiaphers • Species with same isotopic number are called Isodiaphers, e.g., • Isotopic number = mass number – 2 × atomic number .
19K
39,
19 9F
Developments leading to the Bohr’s Model of atom Two developments played an important role in establishment of Bohr’s model of atoms. They are Dual nature of electromagnetic radiations. (wave nature and particle nature) Quantisation of energy
1. 2.
Wave nature of Electromagnetic Radiations •
•
•
•
•
James Maxwell (1870) gave the explanation about the interaction between the charged bodies and the behavior of electric and magnetic fields on macroscopic level. Light and other forms of radiant energy that propagates in the form of waves are called electromagnetic waves or electromagnetic radiations. These waves are produced by a charged body moving in a magnetic field or a magnet moving in an electric field. A wave is a periodic disturbance in space or in a medium that involves elastic displacement of material particles. Radiations which are associated with electric and magnetic field are called electromagnetic radiations.
Coaching for NEET Entrance Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive
6
www.spandanamnews.blogspot.in
PLUS ONE CHAPTEER‐2 ATTOMC STRUCTURE Characte eristics of electromagnetic ra adiations ectromagn netic radiattions have e both ma agnetic as well as electric field d compone ents (a) Ele an nd are not affected a by y electric and a magnetic field. (b) Th hey oscillatte in the phase p perp pendicularr to each other o as w well as perrpendicula ar to the e direction n of propag gation of wave. (c) Ele ectromagn netic waves s do not re equire any medium for f their prropagation n. That me eans the ey can propagate in vacuum. v (d) Ele ectromagn netic radiattions which differ fro om one an nother in tterms of th heir freque ency an nd wavelen ngth. Thes se all type es of electtromagnetiic radiatio ons constiitute whatt as ele ectromagne etic spectrrum. (e) Th he arrange ement of different d t types of electromag e netic radiiations in the orderr of inc creasing wavelength w or decreas sing freque ency in callled electro omagnetic spectrum.. CTERISTIC CS OF WAV VES CHARAC 1.
2.
avelength (λ) : Wa • Distan nce betwee en two adjjacent cres sts or trou ughs is called d wavelengtth. • It is ex xpressed in n angstrom m, (A0) or nanometer n r. 0 -10 -8 -9 - cm • 1A =1 10 m = 10 1 Cm 1nm = 10 0 m or 10-7 Fre equency (γ) • The number n of waves passing p th hrough a point in one seco ond is ca alled freque ency. • Its un nit is Cycles per Seco ond or Herttz , where c is • γ 1λ ie, γ = λ s the velociity of light. (c = 3 ×10 08 m/s )
3.
Ve elocity (C) • The diistance tra avelled by wave w in on ne second is i called ve elocity. • γ, λ an nd C are re elated as c = γ λ • Its un nit is m/s. • For alll electroma agnetic rad diations, C = 3 × 108m/s.
4.
Wa ave numbe er : ( υ ) • The to otal numb ber of wav ve lengths per unit length of a wave is s called wave w numb ber. •
It is eq qual to the e reciproca al of wave length l υ = 1/ λ
It is ex xpressed in cm-1 or m-1. Am mplitude (a) • It is th he height of o a crest or o depth off a trough from the m mean posittion of a wa ave. • It dete ermines th he intensity y of radiatiion. • Intens sity a2 Tim me period d (T) • It is th he time tak ken for the e completio on of one cycle c of a w wave 1 • It is th he reciproc cal of frequ uency. Ie, T = •
5.
6.
γ
•
Its un nit is secon nds per cyc cle (s).
Coaching for NEET Entrance E t and 12th (Chemistr S Special tuittion for 11th ry and Biolo ogy). PH: 9 9895263838 S Sincere – Sy ystematic - Supportiv ve
7
www.spandanamnews.blogspot.in
PLUS ONE CHAPTEER‐2 ATTOMC STRUCTURE Merits off wave the eory plain It can exp • Difffraction : • Intterference :
It is i the bend ding of wav ve around an obstac cle It is i the com mbination of o two wave es of the sa ame or diffferent fre equencies to give a wave who ose distrib bution at each e pointt in space is the algebraic or vector sum s of dis sturbances s at that po oint sulting from m each intterfering wave w res
o Maxwelll’s wave th heory Failure of The theorry failed to o explain • Bla ack body radiation r (e emission of o radiation ns from ho ot bodies) • Ph hotoelectric c effect • Va ariation in heat capac city of mon natomic so olids • Lin ne spectra of atoms Black body radiatiions •
Bla ack-body is i an ideal body whic ch emits an nd absorbs s radiation ns of all fre equencies.
•
Th he radiation ns emitted d by these bodies b are called bla ack body ra adiations.
•
For example when an iron rod is s heated in n a furnac ce, the iron n rod firstt turns red d on ease in tem mperature e the colou ur of rod changes to bright red r to oran nge, furrther incre the en yellow, then white e and finallly blue at the elevated tempera ature.
•
It means th hat the fre equency of emitted radiation goes om a lowe er frequen ncy to a higher h frequency as s the fro tem mperature increases.
•
Th he exact fre equency distribution n of the em mitted radiiation fro om a black k body depe ends only on its tem mperature.
•
At a given temperatu ure, intens sity of rad diation em mitted inc creases with w decre ease of wavelengtth, reache es a ma aximum va alue at a given wav velength and a then starts s dec creasing with w further decrease e of wavelength.
ectric effec ct (H. Hertz)) Photoele •
•
•
•
It is i the proc cess of ejection of electrons fro om the e surface of o a metal,, when ligh ht of suitab ble fre equency strrike on it. Th he emittted elec ctrons a are callled ph hotoelectron ns. a inc cident ra adiation should possess miinimum frrequency to t cause the effect is callled thresh hold freque ency (υ0). the ere is no time t lag between b th he striking g of ligh ht beam and a the eje ection of ellectrons fro om the e surface. Coaching for NEET Entrance E t and 12th (Chemistry S Special tuittion for 11th y and Biolo ogy). PH: 9 9895263838 Sincere – Sy ystematic - Supportiv ve
8
www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE •
•
•
KE →
KE →
•
The number of electrons ejected is proportional to the intensity of incident radiation. The KE of ejected electrons is proportional to the frequency of incident radiation. KE = hυ ‐ hυ0 = h (υ ‐ υ0) Where hυ0 is called work function (wo) The effect is generally shown by the metals having low ionisation enthalpy ( K, Rb & Cs). These explanations could not explain on the basis wave theory. According to wave theory the energy of light depends up on its intensity and not frequency. υo
PLANK’SQUANTUM THEORY OF RADIATION
υ→
Intensity →
According to this theory: 1. Radiant energy is emitted or absorbed not continuously but discontinuously in the form of small packets of energy called quanta. 2. In the case of light, the quantum of energy is called photon 3. Each quantum is associated with a definite amount of energy and it is
proportional to the frequency of light. ie., E υ or E = hυ Where h is a constant, called Plank’s constant h = 6.625 × 10-34 J.s = 6.625 × 10-27 erg.s = 4.136 × 10-15 ev.s 4. A body can emit or absorb energy in terms of integral multiples of quanta ie. E = nhυ where n = 1, 2, 3 ……. ie., A body can absorb or emit energy equal to hυ, 2hυ, 3hυ ….. This theory suggests that light has particle nature. DUAL NATURE OF ELECTROMAGNETIC RADIATION •
The particle nature of light could explain the certain phenomena like photoelectric effect and black body radiation but it was not consistent with the known wave behaviour of light like interference and diffraction.
•
On other hand, the phenomena like diffraction and interference can be explained only on the basis of wave nature of light but it was not consistent with particle behaviour of light like interference and diffraction. ∴ Light has dual nature.
Evidence for the quantized Electronic Energy Levels: Electromagnetic Spectrum The arrangement of different types of electromagnetic radiations in the order of increasing wavelength or decreasing frequency in called electromagnetic spectrum. • radio frequency region around 106 Hz, used for broadcasting. • microwave region around 1010 Hz used for radar. • infrared region around 1013 Hz used for heating. • ultraviolet regionaround 1016 Hz a component of sun’s radiation. • The small portion around 1015 Hz, is what is ordinarily called visible light.
Coaching for NEET Entrance Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive
9
www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE Wavelength increases Cosmic rays | γ-rays | x-rays | uv rays | visible rays |IR rays | microwaves | radio waves Frequency decreases
VISIBLE SPECTRUM • When ordinary light is passed through prism, it split into seven colours. • The arrangement of these colours (VIBGYOR) based on the their frequency is called visible spectrum. • Their frequency ranging from 7.5×1014 (violet) to 4×1014 Hz (red). • One with shorter wavelength bend more (violet) and longer wavelength bend least (red). ATOMIC SPECTRUM Atomic spectrum are two types, they are Emission spectrum & Absorption spectrum. Emission spectrum
Absorption spectrum
•
Spectrum of radiation emitted by the atoms when heat or electric current is passed through gaseous phase of a substance
•
Spectrum of transmitted light after absorption emitted by the atoms when heat or electric current is passed through gaseous phase of a substance
•
Due to de excitation of electrons
•
Due to excitation of electrons
•
Continuous or discontinuous
•
Always discontinuous
•
It gives bright background
•
Dark lines on bright background
lines
on
dark
Hydrogen spectrum Atomic spectrum of hydrogen in obtained by the analysis of the light emitted from the discharge tube containing hydrogen at low pressure using a spectroscope. It consists of six series of lines.
Spandanam
Coaching for NEET Entrance 10 Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE No Series
Ground level (n1)
Excited level (n2)
1
1
2,3,4,…. Ultraviolet region 3,4,5,…. Visible region
2 3 4 5 6
Lymann Series Balmer Series Paschen Series Brackett Series Pfund Series Humphrey Series
2 3
Frequency region
4,5,6,…. Near Infrared region 5,6,7,…. Infrared region 6,7,8,…. Far Infrared region 7,8,9,…. Far Infrared region
4 5 6
Wave no. of spectral lines in the H spectrum can be expressed as,
υ
= R
12
22
cm-1
R is a constant called Rydberg’s constant = 109677cm-1 = 1.09678 × 10-7-m-1 For H like species, the equation is υ = 109677
12
22
z2 cm-1
BOHR’S MODEL OF ATOM Neils Bohr in 1913 modified the Rutherford’s model of atom by applying the principles of quantum theory. The main postulates of Bohr’s model of atom are. An atom consists of a small, heavy positively charged nucleus in the centre and 1. 2. The electrons are revolving around the nucleus in certain selected circular paths called orbits. 3. These orbits are associated with definite energies are known as energy levels. 4. The energy levels are numbered as 1, 2, 3, 4, .. etc or designated as K, L, M, N, O.... etc. 5. As the electron revolves in a particular orbit there is neither absorption nor emission of energy. Therefore these orbits are also called stationary states. 6. When an electron jumps from one orbit to another it will absorb or emit radiation of a definite frequency. The frequency, υ = ΔE = E2 − E1 h h 7. The angular momentum of the electron is a whole number multiple of h , where 2π ‘h’ is Plan’s constant Or angular momentum of electrons in an atom is quantized. That is,
mvr = n
Where, n = 1, 2, 3,....
This expression is called Bohr’s frequency rule.
Coaching for NEET Entrance 11 Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE MERITS OF BOHR’S MODEL 1.
Bohr model explained the stability of the atoms.
2.
It could calculate the energy of the electron in a particular orbit of hydrogen atom. En =
where R is the energy of electron in lowest level (first Bohr orbit)
=
−2.18 × 10 −18 J / atom n2
=
−13.6 eV / atom n2
=
/
−1312 KJ / mol n2
=
For H- like particles (eg : He+, Li2+ etc.)t he expression for energy is En = 3.
It could calculate the radius of orbit of hydrogen atom in which electron rotates.
rn = n 2 a0 ,
Where a0 is the radius of first stationary state of hydrogen called Bohr radius (a0 = 0.529A0 = 52.9 pm)
For hydrogen like particles the radius, rn = Bohr model can explained the velocity of an electron in the nth orbit.
4.
Vn =
where V0 is the velocity of electron in the first Bohr orbit, =2.188 x 108 cm/sec
For H like species, Vn = 5
cm/sec
Bohr model can explained line spectrum of hydrogen.
Explanation for line spectrum of hydrogen by Bohr ΔE = E2 - E1 ΔE =
R
-
But R
E1 =
= R
and
=
∆E
.
=
.
J
=
υ
=
.
JS
= 3.29 × 1015 s-1 υ
= 1.09677×107 m-1
= 2.18×10-18 J υ
E2 =
= 109677 cm-1
Coaching for NEET Entrance 12 Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE LIMITATIONS OF BOHR’S MODEL Demerits 1. He could not explain the fine spectrum of hydrogen 2.
could not explain spectrum of multi electron species.
3.
could not explain electronic repulsions in multi electron atoms.
4.
He could not explain Zeeman effect and Stark effect. Splitting of spectrum lines in Magnetic field is called Zeeman effect Splitting of spectrum lines in Electric field is called Stark effect
5.
He could not explain chemical bonding
6.
He could not explain De-Broglie’s equation (ie. dual nature of matter)
7.
He could not explain Heisenberg’s un-certainity principle
8.
It is applicable to hydrogen like atoms only
TOWARDS QUANTUM MECHANICAL MODEL OF THE ATOM Two important developments leads to the formulation of quantum mechanical model of atom. Dual nature of matter • •
De-Broglie in 1924 proposed that just like light, all the matter should exhibit both particle and wave-like properties ie., dual behaviour. De-Broglie gave an expression for the wavelength and momentum of all material particles. Acco. to Einstein,
E = mc2 …………….(1)
Acco. to plank,
E = hυ………………..(2)
From (1) and(2) mc2 mc2 λ
h = Planck’s constant = 6.626 x 10-34 Js. v = is the velocity p = momentum
= hυ = hc/λ = h/mc = h/mv =h/p
Heisenberg’s Uncertainty principle • Its states that the position and momentum of microscopic moving particles cannot be determined simultaneously with accuracy. mathematically it can be given as Δx × Δp ≥ h • 4π Where, Δx = uncertainty in position Δp = uncertainty in momentum Δp = m x Δv
∴ Δx × m × Δv =
h 4π
Significance 1 it replaced Bohr’s concept of definite orbit by concept of probability. 2 It signifies only for the motion of microscopic objects and is negligible for macroscopic objects.
Coaching for NEET Entrance Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive
13
www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE QUANTUM MECHANICAL MODEL OF ATOM • • •
Quantum mechanics is a theoretical science that takes into account the dual nature of matter. Quantum mechanics was developed independently in 1926 by Werner Heisenberg and Erwin Schrödinger. The fundamental equation of quantum mechanics was developed by Schrödinger, called Schrodinger wave equation. for an atom or a molecule whose energy does not change ∧
with time, the equation is written as H ψ = Eψ . ∧
•
Here H is a mathematical operator called Hamiltonian operator, and ψ is called wave function.
( ψ ) and | ψ |2
•
When Schrödinger equation is solved for a H atom, several solutions are obtained called wave functions or eigen functions.
•
Wave function/amplitude function ( ψ ) has as such no physical significance
•
It is simply a mathematical function of the coordinates of the electron
•
The square of wave function i.e., | ψ |2 is known as probability density which gives the probability of finding an electron at a point within an atom.
•
From the value of | ψ |2 at different points within an atom it is possible to predict the region around the nucleus where electron can most probably be found.
•
This maximum probability region is actually known as atomic orbital.
•
The wave function represent an orbital.
Important Features of the Quantum Mechanical Model of Atom 1.
The energy of electrons in atoms is quantized (i.e., can only have certain specific values).
2.
The existence of quantized electronic energy levels is a direct result of the wave like properties of electrons and are allowed solutions of Schrödinger wave equation.
3.
Both the exact position and exact velocity of an electron in an atom cannot be determined simultaneously (Heisenberg uncertainty principle).
4.
An atomic orbital is the wave function ψ for an electron in an atom
5.
The probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function i.e., | ψ |2. at that point. | ψ |2 is known as probability density and is always positive.
6.
From the value of | ψ |2 at different points within an atom, it is possible to predict the region around the nucleus where electron will most probably be found.
Coaching for NEET Entrance 14 Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE DIFFERENCES BETWEEN ORBIT AND ORBITAL
1
2 3 4
5
Orbit It is the definite circular path around the nucleus where the electrons are revolving It is obtained from Bohr’s theory
1
2
It is 2-dimensional (Planar motion of electrons) Orbits are circular
3
An orbit can accommodate a maximum of 2n2 electrons n = principal quantum number
5
4
Orbital It is the region of space around the nucleus where there is maximum probability to find an electron It is obtained from Heisen-berg’s uncertainty principle It is 3-dimensional (3D motion of electrons) They have different shapes eg:- S orbital is spherical P orbital is dumb-bell shaped An orbital can accommodate only 2electrons
QUANTUM NUMBERS Quantum numbers may be defined as a set of four numbers, which give complete information about an electron present in an atom. There four quantum numbers namely, 1. Principal quantum number (n) 2. Azimuthal quantum number (l) 3. Magnetic orbital quantum number (m) Spin quantum number (s) 4. 1.
Principal quantum number (n) • It indicates the main energy level (orbit) to which the electrons belongs. • It is represented by the letter ‘n’ and can have values n = 1, 2, 3, 4, ... • It helps to calculate size and the energy of orbital • It represents main shell
2.
Azimuthal quantum number/subsidiary/angular momentum quantum number (l) • It indicates the subshell in which the electrons present. • It is represented by the letter by ‘l’ and can have values ‘o’ to (n – 1). • Total no of values 2 + 1
l
0 1 2 3
•
3.
Subshell
Shape of orbital
s p d f
Spherical Dumb-bell Double dumb-bell complex
n=2 n=3 n=4 n=5
l
l
=0
s
= 0, 1
s, p
l
= 0, 1, 2
s, p, d
= 0, 1, 2, 3
s, p, d, f
= 0, 1, 2, 3, 4
s, p, d, f, g
l
l
The orbital angular momentum, mvr of an electron is given by h Where h = h l (l + 1) or l (l + 1) h 2π 2π
Magnetic orbital quantum number (m) • It gives the spatial orientation of the orbital. • It is represented by the letter ‘m’ and can have values - l to + l including zero.
l
0 1 2
n=1
m
No. of orbitals
0 -1, 0, +1 -2, -1, 0, +1, +2
1 3 5
Coaching for NEET Entrance 15 Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive www.spandanamnews.blogspot.in
PLUS ONE CHAPTEER‐2 ATTOMC STRUCTURE 4.
Sp pin quantu um numbe er (s) • • • •
It represe ents the sp pinning of an a electron n. Spinning may be cllockwise orr anticlock kwise. For each value of m, m s can ha ave two vallue. kwise s = +1/2, for an nticlockwis se s = – 1/2. For clock
NODE • •
• •
Th he region orr space aro ound the nucleus n wh here the prrobability of finding an electron n is zerro. No odes are off two types, a) Radial nodes/ spherical nodes n =n–l–1 b) Angullar/ planarr/ nodal planes = ∴ Total num mber of nod des = n – 1 s orbital o has no angula ar nodes
SHAPES OF ATOM MIC ORBIT TALS hat electron ns are not present in a fixed d circular path. The e orbital wave w We know th function for f an elec ctron in an n atom has s no physic cal signific cance. It is s simply a mathemattical function of o the co-o ordinates of o the electtron. Plots of Wave W func ction and Distance w draw a plot of wa ave functio on and disttance for different d orrbitals, then e we find the If we graphs which do no ot come ou ut to be sim milar for alll the orbitals.
S of Wavefunct W tion ( ψ 2) and Dista ance Pots of Square •
forr 1s orbitall the proba ability density is max ximum at the t nucleu us and it decreases d sharply as we w move aw way from it.
•
forr 2s orbitall the proba ability density first decreases d s sharply to zero and again a starts inc creasing. After A reach hing a smalll maxima it decreases again a and approa aches zero as the e value of r increases s further.
•
Th he region where w this probability p y density fu unction re educes to zzero is calle ed nodal surfaces or simply s nod des.
Coaching for NEET Entrance E 16 t and 12th (Chemistr S Special tuittion for 11th ry and Biolo ogy). PH: 9 9895263838 S Sincere – Sy ystematic - Supportiv ve www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE Shape of orbitals s-orbitals • • •
s-orbitals are spherical in shape. so they are unidirectional orientation.(non directional) The size and energy of S-orbital increases with increasing value of principal quantum number ‘n’. Thus
1s < 2s < 3s < 4s . p-Orbitals • p-orbitals are dumb-bell shaped. • It has two lobes. • It is directional. • It has are 3 possible orientation as m = -1, 0, +1 value. • These are designated as px, py, pz in each p-subshells. d-Orbitals • d-orbitals have double dumb-bell shape except d z 2 which has baby shooter like • • • •
shape. It has directional properties. It has are 5 possible orientation as m = -2, -1, 0, +1, +2 values. The five d-orbitals are designated as dxy, dyz, dxz, d x2 − y 2 , d z 2 .
d z 2 has a collar of electron density around its dumb bell called donut.
RULES FOR FILLING ELECTRONS IN AN ATOM 1. Aufbau Principle • It states that, the electrons are added into the various orbitals in order of their increasing energy. • The energy of an orbital is determined by n + l rules. • If two orbitals have same n + l values, then the one with lower ‘n’ value will be filled first. 2. Pauli’s Exclusion Principle • Its states that no two electrons in an atom can have the same set of four quantum numbers ie., an orbital can accommodate a maximum of two electrons. • Upto 3 quantum no. may be same but spin quantum no. n l m s should be different. 1st electron 1 0 0 +1/2 • Eg : two electrons in helium (1s2) have sa values on n, l, 2nd electron 1 0 0 –1/2 m but different s values. 3. Hund’s rule of maximum multiplicity • It states that, no pairing of electron starts in any of the degenerate orbitals until all the orbitals of the subshell contain one electron each with parallel spin.
Coaching for NEET Entrance Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive
17
www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE ELECTRONIC CONFIGURATION OF ATOMS Electronic configuration is the distribution of electrons in to different shells, subshells, and orbits in an atom. The rules which we studied for the filling of electrons help in writing the electronic configuration of different atoms. There are two different ways of writing the electronic configuration of different atoms. Important points • Number of subshell in a principle shell = n • The number of orbitals in a shell = n2 • The maximum number of electrons in a shells = 2n2 • Number of orbitals in subshell = 2l + 1 • Maximum number of electrons in a sub shell = 4 l + 2 EXCEPTIONAL ELECTRONIC CONFIGURATION • •
The fully filled and half filled orbitals have extra stability. Thus p3, p6, d5, d10, f7, and f14 configuration are more stable.
Chromium Expected configuration : Actual configuration :
1s2, 2s2 2p6, 3s2, 3p6, 3d4, 4s2 1s2, 2s2 2p6, 3s2, 3p6, 3d5, 4s1
Copper Expected configuration : Actual configuration :
1s2, 2s2 2p6, 3s2, 3p6, 3d9, 4s2 1s2, 2s2 2p6, 3s2, 3p6, 3d10, 4s1
•
The extra stability of half-filled and completely filled subshell is due to: (i) relatively small shielding, (ii) smaller coulombic repulsion energy (iii) larger exchange energy.
EQUATIONS
•
•
γ=
•
T=1γ
•
γ = 1/λ
•
E = hυ
•
E = nhυ
•
KE
•
wo = hυ0
λ
= hυ ‐ hυ0 = h (υ ‐ υ0)
Coaching for NEET Entrance Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 18 Sincere – Systematic - Supportive www.spandanamnews.blogspot.in
PLUS ONE CHAPTER‐2 ATOMC STRUCTURE •
υ = 109677
•
En =
12
22
z2 cm-1
−18 = −2.18 ×2 10 J / atom
−13.6 eV / atom n2
=
n
•
rn = n 2 a0
or
rn =
•
Vn =
or
Vn =
•
Δx × Δp ≥
=
/
=
−1312 KJ / mol n2
h h Δx × m × Δv = 4π 4π
∧
•
H ψ = Eψ
l (l + 1) •
.
h 2π
or
h =h 2 Where π
l (l + 1) h
Number of subshell in a principle shell = n The number of orbitals in a shell = n2 The maximum number of electrons in a shells = 2n2
Number of orbitals in subshell = 2l + 1
Maximum number of electrons in a sub shell = 4 l +
Spandanam
www.spandanamnews.blogspot.in
Coaching for NEET Entrance Special tuition for 11th and 12th (Chemistry and Biology). PH: 9895263838 Sincere – Systematic - Supportive
19
