JEE NEET Physics Question Bank - Dual Nature of Matter and Radiation

17 Dual Nature of Matter and Radiation
Name of scientist Discovery

Jean perin – Discovered an electron
Milikan – Charge of an electron

J.J.Thomson found the value of
e
–
m

Wilhem Rontgen - discovered X-rays
Henry Bacquerel and Madam curie - Radio activity
Hertz - photo electric effect

Methods of Emission of Electron Ñ
(1) Thermionic Emission : In this method, the current is passed through a filament of metal so
that it gets heated sufficiently and electrons get emitted from the metal.
(2) Field Emission Ñ when a metal is subjected to strong electic field of the order of
108 Vm –1 , electrons are pulled out of the metal surface.

(3) Photo electric emission Ñ when an electromagnetic radiation of enough high frequeney is
incident on a cleaned metallic surface, electrons can be liberated from the metal surface.
This phenomenon is known as the photoelectric effect and electrons so emitted are known
as photo electrons.

Work function (Threshold energy)
The minimum energy required to get emission of an electron ( to eject the free electrons
from metallic surface) is defined as work function of that surface of metal ( I0 ).

I0
hc
hf 0
O0 where f o threshold frequency, O0 threshold wavelength

I0 eV
eOo
hc 12375
Work function in electron volt, §D·
O0 ¨ A ¸
© ¹

(taking planck's constant, h 6.6 u 1034 Js )

Threshold Frequency f0 Ñ The minimum frequency of incindent light for the emission of

photo electrons from metallic surface is defined as threshold frequency f 0 .

447

for the emission of photo electrons, the frequency of the incident light f t f 0

Threshold wave length O0

For the emission of photo electrons from the given metallic surface, the wavelength of incident
light should be some maximum or less than that maximum wavelength. This maximum

wavelength is called the threshold wavelength O0

For emission of photo electrons, O d O0

(1) Effect of intensity of incident light Ñ

By Increasing the intensity of incident light (keeping frequency constant) the number of photo
electrons emitted and hence photoelectric current increases. but the maximum kinetic energy of
photo electrons do not change i.e. value of stopping potential remains unchanged.

? Intensity I v no. of incident photons
v no. of emitted photo electrons in 1 second

D photo electric current

(for a point like source)
1
D 2
distance

1
D distance
(for a linear source)
ivI i
i

(current) 2I
I

(intensity) I V0 0 V

(2) Effect of potential Ñ
l when collector C is kept positive with respect to photo sensitive surface S, the emitted
photo electrons are attracted to collector C and amount of current passing through the
micro ammeter. At certain value of positive potential difference, when all the emitted
electrons are collected, increasing the potential difference further has no effect on the
current. This current is known as saturation current.
when the C is made negative with respect to S, on increasing this negative potential, the
number of photo electrons reaching the collector (value of photo electric current) gradu-
ally decreases.

448

l For some specific negative potential of the collector, even the most energetic electrons are
unable to reach collector, then photo electric current becomes zero. This minimum specific
negative potential of C with respect to S is known as stopping potential or cut off
potential V0

l If the value of stopping potantial is V0 , then the energy required for electron to cross this
potential barrier is, eV0

If maximum speed of photo electron is vmax , then eV0
1
mv 2max
2
(3) Effect of frequency Ñ
If frequency of incident light ! f 0 is increased, the maximum kinetic energy of emitted photo
electrons increased. i.e.the value of stopping potential is also increased but photo electric current
remains constant.
photo electric I 2 ! I1
current I2

f 3 ! f 2 ! f1 ! f 0
I1

saturation current (For
case-1 )
f3 f2 f1

V03 V02 V01 0 V
(4) Effect of photo sensitive surface Ñ
When the photo sensitive surface is changed by keeping frequency and intensity of incident light

constant, the graph of stopping, potential V0 o frequency f found to be straight line and
pasallel to each other. which intersects the X-axis (frequency axis) and the Y-axis at different
points. Which shows that the values of threshold frequencies are different for different metals
§h·
but slope of the graph ¨ ¸ is equal for all the metals.
©e¹

V0

metal-1
T T metal-2
( f 0 )1 ( f0 )2
§1 ·
¨ ¸1 § 1 ·
© O0 ¹ ¨ ¸
© O0 ¹2
f or
1
h( f0 )1 O
e
h( f0 )2
e
It is clear from the graphs, the value of threshold frequency and work function for metal–2 are
more than for metal–1
449

l Einstein's equation for photoelectric effect
The maximum kinetic energy of emitted photo electrons,

K max hf  I0

1 mv 2 hf  hf 0 h f  f0
2 max

hc  hc § ·
hc ¨ 1  1 ¸ Ÿ vmax 2 hc (O0  O )
O O OO0
1 mv 2
O O0 © ¹
max
2 0 m

This equation is called eEinstein's photo electric equation.

l Relation between stopping potential and frequency Ñ

According to definition of stopping potential,

1 2
mvmax eV0
2

§ ·
? eV0 h f  f0 hc ¨ 1  1 ¸
© O O0 ¹

? V0 hc § 1  1 · §
1237 5 ¨ 1  1 ¸
·
e ¨© O O0 ¸¹ © O O 0 ¹

In the graph of V0 o f

V0 h f  f hf
 0
hf
0
e e e

comparing above equation with equation of straight line

y mx  c , slope is found to be h and intercept on X-axis is f0 and intercept on
e

 hf 0
Y-axis is is obtained.
e

(1) The work functions for tungsten and sodium are 4.6 eV and 2.3 eV respectively. If threshold

wavelength for sodium is 5460 A , the value of threshold wavelength for tungsten is
D
.

(A) 10682 A (B) 2730 A (C) 526 A (D) 5892 A
D D D D

(2) The maximum velocity of photo electron emitted from surface of metal is 5 u 106 ms 1 . If specific

charge of an electron is 1.8 u 1011 Ckg –1 then the value of stopping potential is .
(approximately)
(A) 2 V (B) 3 V (C) 7 V (D) 4 V

450

(3) If the intensity of radiation incident on a photo cell be increased by four times, then the number
of photoelectrons and maximum kinetic energy of photoelectrons emitted become ...... .
(A) Four times, doubled (B) Four times, remains unchanged
(C) Doubled, remains unchanged (D) Remains unchanged, Doubled
(4) In a photo cell, with exciting wave length O the maximum speed of emitted photoelectron is v . If
3O
the exciting wave length is changed to the maximum speed of emitted photo electron will be ......
4

(A) greater than (B) (C) less than (D)
4 4 4 3
v v v v
3 3 3 2

(5) Light of wave length 0.6 Pm falls on a surface of metal causes the emission of photoelectrons.
for which the stopping potential is 0.5 V. With light of wavelength 0.4 Pm falls on the same
surface the stopping potential found to be 1.5 V. then the work function of surface of metal is
.
(A) 1.5 eV (B) 0.75 eV (C) 2.5 eV (D) 3 eV
(6) When a certain metallic surface is illuminated with light of wavelength O , the stopping potential
is 4 V0 . When the same surface is illuminated with light of wavelength 2O , the stopping

potential is V0 . The threshold wavelength for the surface is ...... .

O
(A) 6O (B) 8O (C) 3O (D)
4
(7) The frequency of incident light falling on a photosensitive surface is doubled, the value of stopping
potential will be ...... .
(A) Doubled (B) More than doubled
(C) halved (D) less than doubled.
(8) Sodium surface is illuminated by ultraviolet and visible radiation successively and stopping
potantial determined. This stopping potantial is ...... .
(A) Equal in both cases (B) More with visible light
(C) More with ultraviolet light (D) Varies randomly
(9) Light of two different frequencies whose photons have energies 1 eV and 5 eV respectively,
successively illuminates a metal of work function 0.5 eV . The ratio of maximum speed of the
emitted photo electron will be ...... .
(A) 1 : 4 (B) 1 : 1 (C) 1 : 3 (D) 4 : 1

(10) Light of wavelength O falls on a metal having work function O . Where O0 is threshold
hc
0

wavelength of surface of metal. Photo electric effect take place only if
(A) O t O0 (B) O d O0 (C) O 4O0 (D) O t 2O0

451

(11) When the point like sousce is kept 1m away from a photocell, photo electric current 16 mA is
obtained. When the same surface is kept 4m away, the photo electric current will be...... .
(A) 1 mA (B) 2 mA (C) 4 mA (D) 16 mA
(12) The threshold frequency for a metallic surface is f 0 . When radiation of frequency 2 f 0 is
incident on this surface,the maximum speed of emitted photoelectron is found 2 u 106 ms 1 .
When the radiation with frequency 5 f 0 is incident on that, the maximum speed of the emitted
photo electron will be ...... ms1 .

(A) 3 u 106 (B) 6 u 106 (C) 8 u 106 (D) 4 u 106

(13) The kinetic energies of photo electrons emitted from a metal are K1 and K2 , when it is irradiated
with lights of wavelength O1 and O2 respectively. The work function of the metal is

K 2 O2  K1O1 K1K 2 O1O2 K1  K2 O1O2 K2
(A) O1  O2 (B) O  O (C) (D) O  O K
1 2 O1  O2 1 2 1

(14) The work function for a metallic surface is I0 . Now this surface is successively illuminated with
the radiations of energy 5I0 and 10I0 respectively. The ratio of maximum speed of emitted
photo electrons will be ...... .
(A) 1 : 3 (B) 1 : 1 (C) 1 : 2 (D) 2 : 3
(15) The maximum kinetic energy of emitted photoelectron is 0.5 eV when the metal surface is
illuminated with the radiation of frequency 8 u 1014 H z . When the same surface is illuminated with

radiation of frequency 12 u 1014 H z , the maximum kinetic energy of emitted photoelectron is found
to be 2eV. Then the work function of the metallic surface is ...... .
(A) 3.5 eV (B) 0.5 eV (C) 2.5 eV (D) 3.85 eV
(16) The maximum speed of emitted photoelectrons, when light of wavelength O is incident on a
metallic surface having work function I 0 is ...... . where h planck's constant, c speed of
light in vaccum, m mass of electron.

§ 2 hc  OI0 · 2
1
2 hc  OI0
(A) ¨ ¸ (B)
© mO ¹ m

ª 2 hc  OI º2 ª 2 hc  I º 2
1 1

(C) « » (D) « »
« » « »
0 0
mO
¬ ¼ ¬ ¼
m

(17) When a metallic surface is illuminated with light of wavelenght O , the stopping potential is 3 V0
When the same surface is illuminated with light of wavelength 2O , the stopping potential is V0 . The
threhold wavelength for this surface is

(A) 4O (B) 3O (C) 6O (D) O
5
3
452

(18) The work function for aluminium surface is 4.2 eV . The wavelength of incident light for which
the value of stopping potential will be zero ......
h 6.6 u 10 34 Js, c 3 u 108 ms 1
D D D D
(A) 2694 A (B) 2946 A (C) 1854 A (D) 4268 A
(19) The value of threshold frequency for a certain metal is 3.3 u 1014 Hz . If light of frequency

8.2 u 10 Hz is incident on this surface, the value of stopping potential is .
14

h 6.63 u 10 34 Js, e 1.6 u 1019 C.
(A) 2.03 V (B) 3.68 V (C) 1.74 V (D) 4.06 V
(20) The frequency of incident light on a metallic surface is made three times, the maximum kinetic
energy of the emitted photo electrons will become .
(A) three times (B) less than three times
(C) 1/3 times the earlier value (D) more than three times
(21) When the light of frequency 5 u 1014 Hz is incident on a metallic surface having threshold

frequency 4 u 1014 Hz , the photoelectric current found to be 1.8 mA . When the frequency of
incident light is halved and the intensity is made three times, the value of photoelectrics current
will be ...... .
(A) 0.9 mA (B) 5.4 mA (C) 3.6 mA (D) zero
(22) The difference between the maximum kinetic energies of photoelectrons emitted from a metallic
D D
surface by light of wavelength 2000 A and 5000 A will be h 6.6 u 10 34 Js
(A) 3.71 eV (B) 5.94 eV (C) 7.42 eV (D) 2.97 eV
(23) A light with frequency 6 u 1014 Hz is incident on a metal surface whose work function is
1.59 eV .The maximum kinetic energy of photoelectrons emitted will be .....

6.63 u 10
34
h Js

(A) 0.49 eV (B) 0.90 eV (C) 1.26 eV (D) 1.08 eV
(24) The maximum wavelength of radiation that can produce photoelectric effect in certain metal
having work function 3.2 eV will be ...... ( h 6.625 u 10 34 Js )
D D D D
(A) 1988 A (B) 2466 A (C) 2953 A (D) 3881 A
(25) The work function of a photo sensitive surface is 1.6 eV . In order to have the value of stopping
potential equal to 1 V for that surface, the wavelength of the incident light will be in the region of
...... . ( h 6.6 u 10
34
Js )
(A) X-ray region (B) infrared region (C) ultraviolet region (D) visible region

(26) How many photons of radiation of wavelength 5000 A have energy equals to the energy of a
D

photons of . radiations of wavelength 2.5u1013 m ?
(A) 2 u 106 (B) 4 u 106 (C) 8 u 106 (D) 0.5 u 106

453

Ans. Ñ 1 (B), 2 (C), 3 (B), 4 (A), 5 (A), 6 (C), 7 (B), 8 (C), 9 (C), 10 (B), 11 (A),
12 (D), 13 (A), 14 (D), 15 (C), 16 (C), 17 (A), 18 (B), 19 (A), 20 (D), 21 (D),
22 (A), 23 (B), 24 (D), 25 (D), 26 (A)

l Particle like nature of light (photon nature)
Photon is bundles or packet (quanta) of discrete energy. The energy of the smallest packet is
equal to hf .
Properties of photon Ñ

(1) The speed of photon in vaccum is same as speed of light 3 u 10 ms .
8 1

(2) Energy of a photon of frequency f is, E
hc
hf
O

where c velocity of light in vaccum, plank's constant, h 6.6 u 10 34 Js ,
l = wavelength of light.

|
hc 12375 12400
§D· §D·
E in eV
eO taking h = 6.625 u 10-34 Js
O ¨A¸ O ¨A¸
© ¹ © ¹

The energy of photon is not continuous but discrete like hf 2hf ,... which shows the
quantization of energy.
(3) Linear momentum of photon of frequency f is

muc uc
E E hf h
P
c 2 c c O

(4) Rest mass ( m 0 ) of photon is zero, but effective mass,

E hf h
m
c 2
c 2 cO

This mass is also known as kinetic mass of photon.

mass of particle moving with velocity v is, m , where m0 rest mass
m0

1  v2
2

c

but speed of photon in vaccum v = speed of light c

§ 2 ·
? m0 m ¨ 1 v ¸
¨ c 2 ¸¹
0
©

(5) Photon is electrically neutral.
(6) Photons are not effected by electric and magnetic field.
(7) Like a real particle, photon interacts with other particles obeying the law of conservation
of energy and momentum..
454

Number of emitted photons :
The number of photons emitted per second from a source of monochromatic radiation of
wavelength O and power P is given as,

P P PO
hc where E = energy of each photon.
n ;
E hf

Intensity of lght (I) Ñ
Energy crossing per unit area normally per second is called intensity (I) of incident light

?I power)
E P E
(' P
At A t
At a distance ‘r’ from a point source of power P, intensity is given by

P P 1
I ŸIv 2
2
A 4 U r

For a linear source, ÞIµ
P 1
I
2S rl r

where l length of a cylinder at a distance r from the source.

(27) If the efficiency of an electric bulb of 2 W is 20 %, what is number of photons emitted by it in
one second ? the wavelength of light emitted by it is 400 nm. ( h 6.6 u 10 34 Js )

(A) 3.46 u 1016 (B) 4.67 u 1017 (C) 2.52 u 1017 (D) 8.08 u 1017

(28) The monochromatic light of wavelength of 660 nm is produced from He–Ne LASER.Hence,
output power of 6 mW is obtained. If this light is incident on the target, what will be the number

of photons incident per second h 6.6 u 10
34
Js

(A) 4 u 1016 (B) 2 u 1016 (C) 3 u 1016 (D) 5.5 u 1016

D
(29) A source S1 is produsing 1014 photons per second of wavelength 3000 A . Another source S 2 is

producing 1.04 u1014 photons per second of wavelength 3120 A . Then the ratio of powers of
D

sources S1 and S 2 respectively is ...... .

(A) 1 : 1 (B) 1 : 1.02 (C) 1.04 : 1 (D) 1 : 2

(30) 12 u 1012 photons are incident on a surface in 10 s. This photons correspond to a wavelength

12 A . If the surface area of the given surface is 0.02 m 2 . Find the intensity of incident
D

radiations. Velocity of light, c 8 u 108 ms 1 , h 6.6 u 1034 Js

(A) 2.19 u 103 Wm2 (B) 3.48 u 103 Wm2 (C) 9.9 u 103 Wm2 (D) 6.62 u 102 Wm2

455

(31) Monochromatic light of wavelength 6000 A is incident normally on a surface of area 2 cm 2 . If the
D

intensity of light is 200 mWm 2 , find the number of photons being incident on this surface in one
second.
34 8 1
h 6.6 u 10 Js, c 3 u 10 ms
(A) 1.21 u 1014 (B) 3.88 u 1013 (C) 6.16 u 1014 (D) 4.54 u 1013

Ans. Ñ 27 (D), 28 (B), 29 (A), 30 (C), 31 (A)

l Matter Wave (Wave like nature of particle)
According to de-Broglie a moving material particle some times acts as a wave and some times
as a particle.
The wave associated with moving particle is called matter wave or de-Broglie wave and it
propagates in the form of wave packets with group velocity.
(1) de-Broglie wave length :
According to de Broglie theory, the wavelength of de-Broglie wave is given by,

O ŸOv v v
h h h 1 1 1
p mv 2mE P v E
where h planck's constant,
m mass of the particle, v speed of the particle, E = kinetic energy of particle.
(2) de-Broglie wavelength associated with the charged particle :
The kinetic energy of a charged particle accelerated through a potential difference of V

volt, E
1
mv 2 qV .
2

? Hence de-Broglie wavelength, O
h h h
p 2mE 2mqV

12.27 D 0.286 D
O = A , Oproton = A
electron V V
0.202 D 0.101 D
ODeutron = A, O = A
V v  Particle V
(3) de-Broglie wavelength associated with uncharged (netural) particle :
0.286 × 10-10 D
Oneutron =
0.286
m A
E in eV E in eV

Energy of thermal neutron at ordinary temperature

kT Ÿ O
3 h h h
E
2 2mE 2m 3 kT 3mkT
2

where_ T = Absolute temperature, k Boltzmann's constant 1.38 u 1023 JK 1

6.62 × 10-34 25.17 D
?O A
u 1.38 × 10
thermal neutron -27 23 T
3 × 1.67 × 10 T

456

(4) Ratio of wavelength of photon and electron :

hc § hc ·
The wavelength of a photon of energy E is given by,, OP ¨' E ¸
E © O ¹

While the wavelength of an electron of kinetic energy K is given by,

Oe
h
2mK

Op 2
?
c 2mc K
2mK
Oe E E
2

(32) The de-Broglie wavelength of a neutron at 627° C is O . What will be its wavelength at 127° C

O
(A) O (B) 2O (C) O (D)
2 3
3 2 2
(33) If the kinetic energy of a free electron is made thrice, its de-Broglie wavelength will become.......

1
(A) times (B) 3 times (C) 3 times (D) times
1
3 3

(34) The de-Broglie wavelength of a neutron having energy 8 eV is ...... .( h 6.6 u 10
34
Js , mass

of neutron = 1.7 u 1027 kg )

(A) 1 u 1011 m (B) 1.8 u 1011 m (C) 2.2 u 1011 m (D) 0.6 u 1011 m

(35) A proton and a deutron have equal energies. The ratio of their de-Broglie wavelengths is ......

(A) 2 : 1 (B) 1 : 2 (C) 2 :1 (D) 1: 2

(36) A proton and an D  particle are accelerated through same potential difference of 200 V. If de-
Broglie wavelength associated with proton is 5200 A°, then the de-Broglie wavelength associated
with D  particle is ...... .

1300 D
(A) (B) 1300 2 A (C) 2600 A (D) 2600 2 A
D D D
A
2

(37) The linear momentum of an electron intially at rest, accelerated through a potential difference of
25 V is

(A) 5.4 u 1024 kgms 1 (B) 2.7 u 1024 kgms 1

(C) 1.2 u 1024 kgms 1 (D) 3.2 u 1024 kgms1

(38) If the kinetic energy of the particle is increased by 16 times, then the value of de Broglie
wavelength of particle is ...... .
(A) decreased by 75 % (B) increased by 75 %
(C) decreased by 67 % (D) increased by 67 %

457

(39) The de-Broglie wavelength of a proton accelerated through a potential difference of 450 V is
( h 6.6 u 1034 Js, charge of proton 1.6 u 1019 C , mass of proton 1.6 u 1027 kg )

(A) 0.14 u 1011 m (B) 0.2 u 1011 m (C) 0.26 u 1011 m (D) 0.09 u 1011 m

(40) The de Broglie wavelength of a particle moving with a velocity 2.25 u 108 ms1 is equal to the
wavelength of photon. The ratio of kinetic energy of the particle to the energy of the photon is
...... . (velocity of light is c 3 u 108 ms 1 )

(A) 8 (B) 8 (C) 8 (D) 18
7 5 3

(41) The kinetic energy of electron and proton is equal. Then the relation between their de-Broglie
wavelength is

(A) O p ! Oe (B) O p  Oe (C) O p 2Oe (D) O p Oe

(42) An electron and a proton have the same de-Broglie wavelength. Then the kinetic energy of the
electron is ...... .
(A) greater than the kinetic energy of proton (B) less than the kinetic energy of proton.
(C) equal to kinetic energy of proton (D) zero

(43) A body of mass 0.5 kg is moving with a velocity of 1000 ms 1 . The de-Broglie wavelength of
the body is ...... .

(A) 3.32 u 1027 A (B) 1.32 u 1026 A (C) 1.6 u 1027 A (D) 0.132 u 1026 A
D D D D

(44) A particle of mass 1 J has the same de-Broglie wavelength as an electron moving with a

velocity of 2 u 106 ms 1 . The velocity of the particle is .

(A) 1.82 u 1015 ms 1 (B) 3.6 u 1016 ms 1 (C) 3.6 u 1021 ms 1 (D) 9 u 102 ms 1

(45) The velocity of an electron having a wavelength of 10 A is ...... .
D

(A) 7.25 u 106 ms 1 (B) 7.25 u 105 ms 1 (C) 5.25 u 106 ms 1 (D) 4.25 u 105 ms1

(46) Two charged particle of mass 2m andõ 3m have charged 3q andõ 2q respectively. Now both
particles are accelerated through a same potential difference.Then the ratio of their de-Broglie
wavelength is ...... .

(A) 2 : 3 (B) 3 : 2 (C) 1 : 6 (D) 1 : 1

(47) De Broglie wavelength of a proton and D  particle is same. If proton is accelerated through a
potential difference of V volt, then D  particle should be accelerated through a potential
difference of ...... volt.

(A) 1 (B) 8 (C) 2 (D)
1
8

458

(48) The frequency of a photon is 1.5 u 1014 Hz. Its momentum will be ...... . kgms1
Plank's constant h 6.6 10 34 Js, velocity of light c 3 u 108 ms 1 .

(A) 3.3 u 10 28 kgms1 (B) 3.3 u 10 34 kgms1 (C) 3.3 u 10 30 kgms1 (D) 6.6 u 1028 kgms1
(49) An electron of mass m when accelerated through a potential diference of V volt has de-Broglie
wavelength O . The de-Broglie wavelength associated with a proton of mass M accelerated
through the potential difference of 4 V will be ....... .

(A) O M (B) O m (C) O m
(D) O m
2 m 2 M 2M 4 M

D
(50) A photon of wavelength 1.4 A collides with an electron. After the collision the wavelength of
D
proton becomes 2.0 A . Then the energy of scattered electron will be ...... .
(take h 6.63 u 1034 Js )
(A) 4.6 u 10 15 J (B) 4.6 u 10 16 J (C) 3.2 u 10 16 J (D) 2.3 u 10 16 J

(51) To reduce de-Broglie wavelength of an electron from 3 u 1010 m to 1 u 1010 m , its energy
should be ...... .
(A) increased to 9 times (B) increased to 3 times
(C) decreased to third part (D) decreased to nineth part
(52) The rest mass of an electron is m0 . It is moving with the velocity of 0.6 c, its mass m will be ...... .
where c = velocity of light in vaccum.
5m0 4m0 m0
(A) m0 (B) (C) (D)
4 5 6
(53) The potential diference through which an electron should be accelerated so its wavelength will
D
become 0.5 A ...... .
(A) 466 V (B) 747.0 V (C) 941.0 V (D) 602.0 V
(54) The chargless particle neutron has mass of 1.67 u 1027 kg and its kinetic energy is 0.04 eV ,
then calculate de-Broglie wavelength of neutron. h 6.62 u 10
34
Js
D D D D
(A) 1.80 A (B) 1.43 A (C) 2.86 A (D) 3.2 A
(55) De Broglie wavelength associated with an electron moving with the velocity of 105 ms 1 is ...... .

6.6 u 10 34 Js , mass of electron m
31
h 9 u 10 kg
D D D D
(A) 73.33 A (B) 7.33 A (C) 46.2 A (D) 146.66 A

Ans. Ñ 32 (C), 33 (A), 34 (A), 35 (C), 36 (B), 37 (B), 38 (C), 39 (A), 40 (C), 41 (B),
42 (A), 43 (B), 44 (A), 45 (B), 46 (D), 47 (D), 48 (A), 49 (B), 50 (B), 51 (A),
52 (B), 53 (D), 54 (B), 55 (A)

459

Davission and Germer Experiment Ñ
This experiment proves the wave like nature of an electron.
In this experiment using Bragg's law, from the formula 2d sin T nO , the wavelength

found to be 1.67 A . which is near to the de Broglie wavelength of electron ( O 1.65 A ).
D D

Which shows wave like nature of electron.
Heisenberg's Uncertainty principle Ñ
According to Heisenberg's uncertainty principle, If the uncertainty in the x - cordinate of the
position is 'x and uncertainty in the x- cordinate of its momentum is 'p , then

'x 'p t (in one dimension)
h
2S

? ' x ' p t = where
h
=
2S
Now, If 'x o 0 , then Dp ® f
and 'p o 0 then, Dx ® f
Similarly, the uncertainty in the measurements of Energy and time for a particle using above
principle,
'E . 't t =

l If the radius of the nucleus is r then uncertainty in the position of proton inside the nucleus is
'x 2r d

Hence the uncertainty in momentum of proton is.

'p
= = = h
'x d 2r 4S r

For a particle if the uncertainties in the measurement of angular momentum and angular
displacement are 'L and 'T respectively.then from Heisenberg's uncertainty principle,
'L . 'T t =

(56) The correctness of velocity of an electron moving with velocity 50 ms 1 is 0.005 % The
accuracy with which its position can be measured will be ...... .

(A) 46 u 103 m (B) 46 u 104 m (C) 46 u 105 m (D) 46 u 106 m

(57) A proton and electron are lying in a box having unpenitrable walls, the uncertainty in their
momenta will be ...... .

(A) For proton is more, as compared to electron (B) For electron is more, as compared to the proton

(C) same for both the particles (D) directly proportional to their masses

460

(58) The maximum uncertainty in the position of proton is 6 u 108 m , then the minimum uncertainty

in its velocity will be ...... .( h 6.625 u 10
34
Js , mass of proton = 1.67 u 10
27
kg )

(A) 1 mms 1 (B) 1 ms 1 (C) 1 cms 1 (D) 100 ms 1

(59) If the uncertainty in the position of an electron is 1010 m , then the value of uncertainly in its

momentum (in kg ms1 ) will be

(A) 1.054 u 1024 (B) 1.112 u 1024 (C) 1.054 u 1022 (D) 1.112 u 1022

Ans. Ñ 56 (A), 57 (C), 58 (B), 59 (A)
Assertion - Reason type Question :

Instruction : Read assertion and reason carefully, select proper option from given below.

(a) Both assertion and reason are true and reason explains the assertion.

(b) Both assertion and reason are true but reason does not explain the assertion.

(c) Assertion is true but reason is false.

(d) Assertion is false and reason is true.
(60) Assertion Ñ The work function of a metal is 2 eV . To have photo emission from the surface of
the metal, the maximum wavelength of incident photon is 6200 A°.

Reason Ñ Work function, )
hc
Omax

(A) a (B) b (C) c (D) d
(61) Assertion Ñ Light with frequency which is1.3 times the threshold frequency is incident on a photo
sensitive surface. Now, the frequency of incident light is halved and the intensity is
doubled, the photo electric current remains unchanged.
Reason Ñ Photo electric current is directly proportional to the intensity of incident light.
(A) a (B) b (C) c (D) d
(62) Assertion Ñ Proton is nearly heavier by 1840 times than an electron. A proton is accelerated
through a potential difference of 1 kV, Its kinetic energy becomes 1 keV
Reason Ñ Kinetic energy gained = (charge) × (potential difference)
(A) a (B) b (C) c (D) d
(63) AssertionÑ The kinetic energy of photoelectrons emitted from the photo sensitive surface
depends on the frequency of the incident light.
Reason Ñ Kinetic energy of emitted photoelectrons changes with the change in the frequency of
incident light.
(A) a (B) b (C) c (D) d

461

(64) Assertion Ñ On increasing the frequency of incident light, the number of emitted photons remains
constant.
Reason Ñ the number of emitted photo electrons does not depend on the frequency of incident light,
but depends on the intensity.
(A) a (B) b (C) c (D) d
(65) Assertion Ñ An electron and a proton are accelerated through same potential difference. The de
Broglie wavelength associated with an electron is more than the de- Broglie
wavelength associated with proton.
Reason Ñ The de-Broglie wavelength associated with the charged particle accelerated through a

potential difference of V volt is given by, O v 1
h
2mqV m (for equal value of qV ).
(A) a (B) b (C) c (D) d
(66) Assertion Ñ A radiation of monochromatic light (with enough high frequency) is incident on a
metallic surface. The kinetic energy of emitted photoelectrons is lying between
0 to K max .
Reason Ñ The value of work function changed with the depth from the surface of metal.
(A) a (B) b (C) c (D) d
(67) Assertion Ñ The de-Broglie wavelength associated with molecules is inversely proportional to the
square root of the absolute temperature.
Reason Ñ The value of vrms for moleaules depends on the absolute temperature.
(A) a (B) b (C) c (D) d
Ans Ñ 60 (A), 61 (D), 62 (A), 63 (A), 64 (A), 65 (A), 66 (C) 67 (A)
Comprehension Type Questions :
paragraph Ñ

The work function of ceisium metal is 2.14 eV . When radiation of frequency 6 u 1014 H z is
made incident on it, then photoelectrons are emitted. Answer the following questions Ñ
(68) Maximum kinetic energy of photoelectron ...... .
(A) 5.58 u 10 20 J (B) 3.34 u 1019 (C) 5.58 u 10 18 J (D) 3.34 u 10 20 J
(69) The value of stopping potential ...... .
(A) 0.236 V (B) 0.349 V (C) 1.03 V (D) 0.87 V
(70) maximum speed of photo electrons ...... .
(A) 155 u 103 ms 1 (B) 224 u 103 ms1 (C) 3.50 u 105 ms1 (D) 276 u 103 ms 1
(71) The value of threshold wavelength ...... .
D D D D
(A) 4647 A (B) 3288 A (C) 5789 A (D) 6134 A
(72) The value of threshold frequency ...... .

(A) 5.18 u 1014 Hz (B) 4.44 u 1014 Hz (C) 5.56 u 1018 Hz (D) 4.89 u 1014 Hz

462

(73) The variation of intensity (I)of incident radiation with photo electric current (i) can be shown by
...... . i i

(A) (B)

I I

i i

(C) (D)

I I

Ans. : 68 (C), 69 (B), 70 (C), 71 (C), 72 (A), 73 (A)

Graphical questions Ñ
(74) Which of the following graph represents the variation of particle momentum and the associated
de-Broglie wavelength
(A) p (B) p

O O
(C) p (D) p

O O

(75) According to Einstein's photoelectric equation, the graph between the kinetic energy of photoelec-
trons ejected and the frequency light is
K K
(A) (B)

f f

463

(C) K (D) K

f f

(76) In the graph shown below, V2 ! V1 then ...... .

where V potential difference, i o photoelectric current
i

(A) O1 O2 (B) O1  O2

(C) O1 O2 (D) O1 ! O2

O2

O1
V2 V1 V

(77) The anode voltage of a photocell is kept fixed. The wavelength of the light falling on the
cathode is gradually changed.The plate current (I) of the photocell varies as follows.

(A) I (B) I

0 O 0 O

(C) I (D) I

0 O O
0

Ans. : 74 (D), 75 (D), 76 (D) 77 (A)

464

Match the columns :
(78) Methods for eomission of electron are shown in column-1 and in column-2 methods to obtain it
are shown. Match the columns.

column-1 column-2

(a) Thermionic emission (p) By incidenting suitable light

(b) photo electric emission (q) By heating (by passing current through

filament)

(c) Field emission (r) By colliding accelerated electron beam on
the surface of the metal.

(d) Secondary emission (s) By appying strong electric field.

(A) a o q b o p c o s d o r
(B) a o p b o q c o r d o s
(C) a o r b o s c o p d o q
(D) a o s b o r c o q d o p
(79) In column-1 physical quantities related to photoelectric effect are shown. Join them with
appropriate physical quantitces given in column-2.

column-1 column-2

(a) saturation current (p) Frequency of incident light

(b) stopping potential (q) work function

(c) de Broglie wavelength associated (r) Area of photo sensitive surface

with photo electron

(d) Force exerted on photo sensitive (s) Intensity of incident light

surface due to incident radiation. (For constant frequency)õ

(A) a o s b o p, q c o p, q d o p, r, s
(B) a o r, p b o s, r c o r d o q
(C) a o p b o r c o r, s d o s
(D) a o s b o r c o q d o p
Ans. Ñ 78 (A), 79 (A)

l

465