i Principal quantum number n : Proposed by Bohr It describes the size of the electron wave and the total energy of the electron.. The wavelength of a spectral line for an electronic tran
Trang 1Topic Page No.
Jhalawar Road, Kota, Rajasthan (324005)
Syllabus
Bohr model, spectrum of hydrogen atom, quantum numbers; Wave-particle duality, de-Broglie hypothesis; Uncertainty principle; Qualitative quantum mechanical picture of hydrogen atom, shapes of s, p and d orbitals; Electronic configurations
of elements (up to atomic number 36); Aufbau principle; Pauli ’ s exclusion principle and Hund ’ s rule .
Name : Contact No
Trang 2ATOMIC STRUCTURE
KEY CONCEPTS
Electromagnetic Wave Radiation :
The oscillating electrical/magnetic field are electromagnetic radiations Experimentally, the direction of oscillations
of electrical and magnetic field are prependicular to each other
Wavelength () : Wavelength of a wave is defined as the distance between any two consecutive crests
or troughs It is represented by (lambda) and is expressed in Å or m or cm or nm (nanometer) or pm(picometer)
1 Å = 10– 8 cm = 10–10 m
1 nm = 10– 9 m, 1 pm = 10–12 m
Frequency () : Frequency of a wave is defined as the number of waves passing through a point in one
second It is represented by (nu) and is expressed in Hertz (Hz) or cycles/sec or simply sec–1 or s–1
1 Hz = 1 cycle/sec
v = ×
Quantum Theory of Light :
The smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation is called
as quantum of light
h = 6.626 x 10–34 J-Sec (h - Planck const.) E0 =
hc (c - speed of light) ( - wavelength)
Order of magnitude of Eo = 10
8 3410
1010
= 10–16 J
One Electron Volt (e.v.) :
Energy gained by an electron when it is accelerated from rest through a potential difference of 1 volt
1eV = 1.6 x 10–19J
For each metal, there is a characteristic minimum frequency, 0 (also known as threshold frequency) below
which photoelectric effect is not observed At a frequency > 0, the ejected electrons come out with certainkinetic energy The kinetic energies of these electrons increase with the increase of frequency of the lightused
2 2mKZe4
hn
Velocity of an Electron in Bohr ’ s Orbit :
n1
Trang 3kme
Z
eV / atom n T.E. ; Z T.E.
= – 2.18 × 10–18 2
2n
Z J/atom
Relation Between P E., K E & T E :
2
P.E
T.E.
Definition Valid for Single Electron System :
(i) Ground state :
Lowest energy state of any atom or ion is called ground state of the atom It is n = 1
Ground state energy of H–atom = – 13.6 ev
Ground state energy of He+
on = – 54.4 ev
(ii) Excited State :
States of atom other than the ground state are called excited states :
n = 2 first excited state
n = 3 second excited state
n = 4 third excited state
n = n + 1 nth excited state
(iii) Ionisation energy (IE) :
Minimum energy required to move an electron from ground state to
n = is called ionisation energy of the atom or ion
onisation energy of H–atom = 13.6 ev
onisation energy of He+ ion = 54.4 ev
onisation energy of Li+2 ion = 122.4 ev
Line Spectrum of Hydrogen :
Wave number,
1 = =
2 1
2n
1n
1RZ
R = Rydberg constant = 1.09678 × 107m–1; R ~1.1 × 107 m–1 ; R =
hc
eV6.13
; R ch = 13.6 eV
Spectra lines of Hydrogen Atom :
Lyman Series
It is first spectral series of H
It was found out in ultraviolet region in 1898 by Lyman
It’s value of n1 = 1 and n2 = 2,3,4 where ‘n1’ is ground state and ‘n2’ is called excited state of
electron present in a H - atom
Trang 4Balmer Series :
It is the second series of H-spectrum
It was found out in 1892 in visible region by Balmer
It’s value of n1 = 2 and n2 = 3,4,5,
Paschen Series :
It is the third series of H - spectrum
It was found out in infrared region by Paschen
It’s value of n1 = 3 and n2 = 4,5,6
Brackett Series :
It is fourth series of H - spectrum
It was found out in infrared region by Brackett
It’s value of n1 = 4 and n2 = 5,6,7
Pfund Series :
It is fifth series of H- spectrum
It was found out in infrared region by Pfund
It’s value of n1 = 5 and n2 = 6,7,8 where n1 is ground state and n2 is excited state
Humphry Series :
It is the sixth series of H - spectrum
It was found out in infrared region by Humphry
It’s value of n1 = 6 and n2 = 7 , 8 , 9
Wave Mechanical Model of Atom :
Dual nature of electron (de-Broglie Hypothesis):
Heisenberg ’ s Uncertainty Principle :
The exact position and momentum of a fast moving particle cannot be calculated precisely at the samemoment of time If x is the error in the measurement of position of the particle and if p is the error inthe measurement of momentum of the particle, then:
x p
4
h
or x (mv)
4h
Schrodinger wave equation :
y + 2
2z
+ 22h
m
8 (E - V) = 0where x, y and z are three space coordinates
m is the mass of electron
Trang 5Quantum Numbers :
The set of four numbers required to define an electron completely in an atom are called quantum numbers.The first three have been derived from Schrodinger wave equation
(i) Principal quantum number (n) : (Proposed by Bohr)
It describes the size of the electron wave and the total energy of the electron It has integral values
1, 2, 3, 4 , etc., and is denoted by K, L, M, N , etc
Number of subshell present in nth shell = n
Number of orbitals present in nth shell = n2
The maximum number of electrons which can be present in a principal energy shell is equal to 2n2
No energy shell in the atoms of known elements possesses more than 32 electrons
Angular momentum of any orbit =
2nh
(ii) Azimuthal quantum number () : (Proposed by Sommerfield)
It describes the shape of electron cloud and the number of subshells in a shell
It can have values from 0 to (n – 1)
Number of orbitals in a subshell = 2 + 1
Maximum number of electrons in particular subshell = 2 × (2 + 1)
Orbital angular momentum L =
2
h
)1(
h
i.e Orbital angular momentum of s orbital = 0, Orbital angular momentum of p orbital =
2
h
2 ,
Orbital angular momentum of d orbital =
2
h3
(iii) Magnetic quantum number (m) : (Proposed by Linde)
It describes the orientations of the subshells It can have values from – to + including zero, i.e.,total (2 + 1) values Each value corresponds to an orbital s-subshell has one orbital, p-subshellthree orbitals (px, py and pz), d-subshell five orbitals (dxy,dyz,dzx,dx 2y 2,dz 2) and f-subshell hasseven orbitals The total number of orbitals present in a main energy level is ‘n2
’
(iv) Spin quantum number (s) : (Proposed by Samuel Goldsmit & Uhlenbeck)
It describes the spin of the electron It has values +1/2 and –1/2 signifies clockwise spinning and anticlockwisespinning
Spin magnetic moment s = 2ehmc
s(s1) or = n(n2) B.M (n = no of unpairedelectrons)
It represents the value of spin angular momentum which is equal to
2
h
)1s(
s
Maximum spin of atom =
21
x No of unpaired electron
Trang 6PART - I : OBJECTIVE QUESTIONS
* Marked Questions are having more than one correct option.
Section (A) : Nucleus, Plancks Quantum Theory, Photoelectric effect
A-1. The study of cathode rays (i.e electronic discharge through gases) shows that
-(A) Alpha particles are heavier than protons (B) All forms of matter contain electrons
(C) All nuclei contain protons (D) e/m is constant
A-2. Proton is
-(A) Nucleus of deuterium (B) Ionised hydrogen molecule
(C) Ionised hydrogen atom (D) An -particle
A-3. Which is not deflected by magnetic field
-(A) Neutron (B) Positron (C) Proton (D) Electron
A-4. The ratio of the "e/m" (specific charge) values of a electron and an particle is
A-5. The element having no neutron in the nucleus of its atom is
(A) Hydrogen (B) Nitrogen (C) Helium (D) Boron
A-6. Cathode rays are
-(A) Electromagnetic waves (B) Radiations
(C) Stream of -particles (D) Stream of electrons
A-7.* Which of the following is iso-electronic with neon?
A-8. The approximate size of the nucleus of 6428Ni is :
A-9. The value of Planck’s constant is 6.63 × 10–34 Js The velocity of light is 3 × 108 m/sec Which value is
closest to the wavelength of a quantum of light with frequency of 8 × 1015 sec–1 ?
(A) 5 × 10–18 m (B) 4 × 10–8 m (C) 3 × 107 m (D) 2 × 10–25 m
A-10. According to Dalton’s atomic theory, an atom can –
(C) Neither be created nor destroyed (D) None
A-11. Rutherford’s experiment on scattering of alpha particles showed for the first time that atom has
-(A) Electrons (B) Protons (C) Nucleus (D) Neutrons
A-12. - particles are represented by –
(A) Lithium atoms (B) Helium nuclei (C) Hydrogen nucleus (D) None of these
A-13. The MRI (magentic resonance imaging) body scanners used in hospitals operate with 400 MHz radio frequency
energy The wavelength corresponding to this radio frequency is
Trang 7A-14. Electromagnetic radiations of wavelength 242 nm is just sufficient to ionise Sodium atom Then the ionisation
energy of Sodium in kJ mole-1 is
A-15. Light of wavelength falls on metal having work function hc/0 Photoelectric effect will take place only if :
(A) 0 (B) 20 (C) 0 (D) 0/2
A-16. Photon of which light has maximum energy :
A-17. The ratio of the energy of a photon of 2000 Å wavelength radiation to that of 4000 Å radiation is
A-18. A photon of energy h is absorbed by a free electron of a metal having work function w < h Then :
(A) The electron is sure to come out
(B) The electron is sure to come out with a kinetic energy (h– w)
(C) Either the electron does not come out or it comes with a kinetic energy (h– w)
(D) It may come out with a kinetic energy less than (h– w)
A-19. A bulb of 40 W is producing a light of wavelength 620 nm with 80% of efficiency then the number of photons
emitted by the bulb in 20 seconds are (1eV = 1.6 × 10–19 J, hc = 12400 eV Å)
(A) 2 × 1018 (B) 1018 (C) 1021 (D) 2 × 1021
Section : (B) : Bohr Model
B-1. The shortest wavelength of He atom in Balmer series is x, then longest wavelength in the Paschen series of Li+2
x 16
(C) 5
x
(D) 9 x
B-2. Correct order of radius of the st orbit of H, He+, Li2+, Be3+ is :
B-5. What is likely to be orbit number for a circular orbit of diameter 20 nm of the hydrogen atom if we assume
Bohr orbit to be the same as that represented by the principal quantum number ?
Trang 8B-9. The frequency of line spectrum of sodium is 5.09 x 10 sec–1 Its wave length (in nm) will
be- [c = 3 × 108
B-10. The species which has its fifth ionisation potential equal to 340 V is
B-11. Match the following
(A) Energy of ground state of He+ (i) + 6.04 eV
(B) Potential energy of orbit of H-atom (ii) –27.2 eV
(C) Kinetic energy of excited state of He+ (iii) + 54.4 V
(D) Ionisation potential of He+ (iv) – 54.4 eV
(A) A – (i), B – (ii), C – (iii), D – (iv) (B) A – (iv), B – (iii), C – (ii), D – (i)
(C) A – (iv), B – (ii), C – (i), D – (iii) (D) A – (ii), B – (iii), C – (i), D – (iv)
B-12. In a certain electronic transition in the hydrogen atoms from an initial state (A) to a final state (B), the difference
in the orbital radius (r1– r2) is 24 times the first Bohr radius Identify the transition
(A) 5 1 (B) 25 1 (C) 8 3 (D) 6 5
B-13 S 1 : Bohr model is applicable for Be2+ ion
S 2 : Total energy coming out of any light source is integral multiple of energy of one photon.
S 3 : Number of waves present in unit length is wave number.
S 4 : e/m ratio in cathode ray experiment is independent of the nature of the gas.
(A) F F T T (B) T T F F (C) F T T T (D) T F F F
B-14. On Bohr’s stationary orbits
-(A) Electrons do not move (B) Electrons move emitting radiations
(C) Energy of the electron remains constant (D) Angular momentum of the electron is h/2
B-15. The value of Bohr radius of hydrogen atom is
-(A) 0.529x 10–7cm (B) 0.529x 10-8cm (C) 0.529x 10-9cm (D) 0.529x 10–10 cm
B-16. On the basis of Bohr’s model, the radius of the 3rd orbit is
-(A) Equal to the radius of first orbit (B)Three times the radius of first orbit
(C) Five times the radius of first orbit (D) Nine time the radius of first orbit
B-17. Supposing the energy of fourth shell for hydrogen atom is - 50 a.u (arbitrary unit) What would be its ionization
B-20. For ionising an excited hydrogen atom, the energy required in eV will be
-(A) 3.4 or less (B) More than 13.6 (C) Little less than 13.6 (D) 13.6
B-21. A gas absorbs a photon of 300 nm and then re-emitts two photons One photon has a wavelength 600 nm
The wavelength of second photon is
Trang 9B-22. The ratio of difference in wavelengths of 1 and 2 lines of Lyman series in H–like atom to difference in wavelength
for 2nd and 3rd lines of same series is:
(A) 2.5 : 1 (B) 3.5 : 1 (C) 4.5 : 1 (D) 5.5 : 1
B-23. If radius of second stationary orbit (in Bohr's atom) is R Then radius of third orbit will be
B-24. The velocity of an electron in the third orbit of hydrogen atom
-(A) 7.28 x107 cm sec–1 (B) 7.08 x 107 cm sec –1
(C) 7.38 x 107cm sec–1 (D) 7.48 x107cm sec–1
B-25. The ionization energy of a hydrogen atom is 13.6eV The energy of the third-lowest electronic level in doubly
ionized lithium (Z = 3) is
-(A) –28.7 eV (B) –54.4 eV (C) –122.4 eV (D) –13.6 eV
B-26. The momentum of a photon with energy 20 eV is
-(A) 10.66 x 10–27 Kg m sec–1 (B) 10.55 x 10–27 Kgm sec–1
(C) 10.60 x 10–27 Kgm sec–1 (D) 10.80 x 10–27 Kgm sec–1
B-27. The energy of hydrogen atom in its ground state is –13.6 eV The energy of the level corresponding to n = 5 is:
(A) –0.54 eV (B) –5.40 eV (C) –0.85 eV (D) –2.72 eV
B-28. Three energy levels P, Q, R of a certain atom are such that EP < EQ < ER If 1, 2 and 3 are the wave length
of radiation corresponding to transition R Q ; Q P and R P respectively The correct relationshipbetween 1, 2 and 3 is
(A) 1 + 2 = 3 (B)
2 1 3
1 1 1
1 1 2
Section : (C) : Spectrum/Spectral lines
C-1. The wavelength of a spectral line for an electronic transition is inversely proportional to :
(A) number of electrons undergoing transition
(B) the nuclear charge of the atom
(C) the velocity of an electron undergoing transition
(D) the difference in the energy involved in the transition
C-2. No of visible lines when an electron returns from 5th orbit to ground state in H spectrum :
C-3. Number of possible spectral lines which may be emitted in bracket series in H atom, if electrons present in
9th excited level returns to ground level, are
4R
Trang 10C-7. The wave number of the first line of Balmer series of hydrogen is 15200 cm The wave number of the first
Balmer line of Li2+ ion
is-(A) 15200cm–1 (B) 60800 cm–1 (C) 76000 cm–1 (D) 136800 cm–1
C-8. Suppose that a hypothetical atom gives a red, green, blue and violet line spectrum Which jump according
to figure would give off the red spectral line
(A) 3 1 (B) 2 1 (C) 4 1 (D) 3 2
C-9. The wavelength of the third line of the Balmer series for a hydrogen atom is
-(A)
HR100
21
(B)
HR 21
100
(C) 100
21RH
(D) 21100RH
C-10. Wave number of a spectral line for a given transition is x cm–1 for He+ , then its value for Be3+ for the same
transition is
-(A) 4x cm–1 (B) x cm–1 (C) x/4 cm–1 (D) 2x cm–1
C-11. What is the change in the orbit radius when the electron in the hydrogen atom (Bohr model) undergoes the
first Paschen transition
C-14. If the shortest wavelength of H atom in Lyman series is x, then longest wavelength in Balmer series of He+
x
(C) x
59x
C-15. A photon was absorbed by a hydrogen atom in its ground state and the electron was promoted to the fifth
orbit When the excited atom returned to its ground state, visible and other quanta were emitted Other quantaare -
(A) 2 1 (B) 5 2 (C) 3 1 (D) 4 1
C-16. In a sample of H-atom electrons make transition from 5th excited state to ground state, producing all possible
types of photons, then number of lines in infrared region are
Trang 11Section : (D) Debroglies hypothesis and Heisenbergs Uncertainty principle
D-1. An -particle is accelerated through a potential difference of V volts from rest The de-Broglie’s wavelength
286.0
(C) ÅV
101.0
(D) ÅV
983.0
D-2. de-Broglie wavelength of electron in second orbit of Li2+ ion will be equal to de-Broglie of wavelength of electron
in
(A) n = 3 of H-atom (B) n = 4 of C5+ ion (C) n = 6 of Be3+ ion (D) n = 3 of He+ ion
D-3. A ball has a mass of 0.1 kg its velocity is 40 m/s, find out de Broglie wave length
-(A) 1.66 x 10–34m (B) 2 x 10–34 m (C) 3 x 10–34 m (D) 4 × 10–34 m
D-4. If the uncertainty of position for an electron is zero, what is the uncertainty of the
D-5. In an electron microscope, electron are accelerated to great velocities Calculate the wavelength of an electron
travelling with a velocity of 7.0 megameters per second The mass of an electron is 9.1×10-28 g (A) 1.0 × 10–13m (B) 1.0 × 10–7m (C) 1.0 m (D) 1.0 × 10–10m
-D-6. What possibly can be the ratio of the de Broglie wavelengths for two electrons each having zero initial energy
and accelerated through 50 volts and 200 volts ?
D-7. In H-atom, if ‘x’ is the radius of the first Bohr orbit, de Broglie wavelength of an electron in 3rd orbit is:
(A) 3 x (B) 6 x (C)
2x9
(D) 2x
D-8. Which of the following is the most correct expression for Heisenberg's uncertainty principle
D-11. Velocity of helium atom at 300 K is 2.40 x 102 meter per sec What is its wave length
-(mass number of helium is 4)
(A) 0.416 nm (B) 0.83 nm (C) 803 Å (D) 8000Å
Trang 12Section (E) Quantum theory
E-1. An electron has a spin quantum number + 1/2 and a magnetic quantum number –1 It cannot be
present in
-(A) d-Orbital (B) f-Orbital (C) s-Orbital (D) p-Orbital
E-2. If the electronic structure of oxygen atom is written as 1s2, 2s2 it would violate
-(A) Hund’s rule (B) Paulis exclusion principle
(C) Both Hund’s and Pauli’s principles (D) None of these
E-3. The dsubshell is
-(A) 5 - Fold degenerate (B) 3-Fold degenerate (C) 7-Fold degenerate (D) Non- degenerate
E-4. The energy of an electron of 2py orbital is
-(A) Greater than 2px orbital (B) Less than 2pz orbital
(C) Equal to 2s orbital (D) Same as that of 2px and 2pz orbitals
E-5. In which of the following pairs is the probability of finding the electron in xy-plane zero for both
orbitals ?
(A) dyz, dx 2 – y 2 (B) pz,dz2 (C) 4dzx, 3pz (D) All of these
E-6. The number of unpaired electrons in carbon atom is
The above configuration is not correct as it violates
-(A) Only Hund’s rule (B) Only Pauli’s exclusion principle
(C) (n + l) rule (D) (Hund + Pauli) rule
E-11. d6 configuration will result in total spin of
Trang 13PART - II : MISCELLANEOUS QUESTIONS
Comprehensions Type
Comprehension # 1
The only electron in the hydrogen atom resides under ordinary conditions on the first orbit Whenenergy is supplied, the electron moves to higher energy shells depending on the amount of energyabsorbed When this electron returns to any of the lower energy shells, it emits energy Lyman series
is formed when the electron returns to the lowest energy state while Balmer series is formed wen theelectron returns to second energy shell Similarly, Paschen, Brackett and pfund series are formedwhen electron returns to the third, fourth and fifth energy shells from higher energy shells respectively.Thus, the different spectral lines in the spectra of atoms correspond to different transitions of electronsfrom higher energy levels to lower energy levels
1. If the shortest wavelength of H atom in Lyman series is x, then longest wavelength in Balmer series
36 x
(C) 4
x
(D) 9
5 x
2. The ratio of the number of spectral lines obtained when an electron jumps from 7th level to ground
state to 6th level to 3rd level
The French physicist Louis de Broglie in 1924 postulated that matter, like radiation, should exhibit
a dual behaviour He proposed the following relationship between the wavelength of a material particle,its linear momentum p and planck constant h
= p
h = mv h
The de-Broglie relation implies that th wavelength of a particle should decreases as its velocity increase
It also implies that for a given velocity heavier particles should have shorter wavelength than lighterparticles The waves associated with particles in motion are called matter waves or de Broglie waves.These waves differ from the electromagnetic waves as they
(i) have lower velocities
(ii) have no electrical and magnetic fields and
(iii) are not emitted by the particle under consideration
The experimental confirmation of the de Broglie relation was obtained when Devisson and Gerner, in
1927, observed that a beam of electron is diffracted by a nickel crystal As diffraction is a characteristicproperty of waves, hence the beam of electron behaves as a wave, as proposed
h i.e
x (mv) h
Trang 144. If the uncertainty in velocity and position is same, then the uncertainity in momentum will be:
(A)
4
hm
(B) m
4
h
(C)
m 4
h
(D)
4
h m 1
5. Two particles A and B are in motion If the wavelength associated with the particle A is 5.0 × 10–8 m, the
wavelength of particles B having momentum half of A
is-(A) 2.5 × 10–8 m (B) 1.25 × 10–8 m (C) 1.0 × 10–7 m (D) 1.0 × 10–8 m
6. The uncertainty in the position of an electron (mass = 9.1 × 10–28 g) moving with a velocity of
3.0 × 104 cm s–1 accurate upto 0.011% will be
On the contrary particle nature of electron was
established on the basis of photoelectric effect When a photon strikes the metal surface, it gives up itsenergy to the electron Part of this energy (saw W) is used by the electrons to escape from the metal and theremaining imparts the kinetic energy ( 1 2)
2 mu to the photoelectron The potential applied on the surface toreduce the velocity of photoelectron to zero is known as stopping potential
7. The wavelength of helium atom whose speed is equal to its rms speed at 27ºC :
9. The wavelength of a golf ball weighing 200g and moving at a speed of 5m/hr is of the order
n l and m These quantum numbers describe the energy level of an orbital and define the shape and
orientation of the region in space where the electron will be found
10. Which quantum number determines orientation of the electron ?
(A) Principal (B) Secondary (C) Magnetic (D) Spin
11. Radial nodes are maximum in
12. Consider following statements
A Splitting of spectral line occurs when placed in a magnetic field or in an electric field
B In case of 1s-orbital, the density of the charge cloud is the greatest at the nucleus and falls off with thedistance The density ( at a particular distance) is uniform
C Electron-density is concentrated along a particular direction in case of 2p-orbital
D A p-orbital can take maximum of six electrons
Select the correct option
Trang 15Match the column
(i) Aufbau principle (a) Line spectrum in visible region
(iii) Alpha particles (c) Electromagnetic radiation
15. Frequency = f, Time period = T, Energy of nth orbit = En , radius of nth orbit = rn , Atomic number = Z,
(iv) In a single isolated H-atom for 31 transition (d) 2nd line has wave number
16
R3
(e) Total number of spectral line is 10