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Chapter-11 DUAL NATURE OF MATTER

AND RADIATION

Work function (jo): The minimum energy required for an electron to escape from the

surface of a metal

i.e. The energy required for free electrons to escape from the metal surface

Work function of alkali metals is

less as compared to other metals.

Work function of metals decreases

with increase in atomic number.

Work function depends on the properties of the metal and nature of the surface.

Cesium is the best photosensitive metal as it has least Work function.

Infrared radiation can not produce photoelectric effect on any metal surface

The phenomenon of emission of electrons from metal surfaces exposed to light energy of

suitable frequency is called

photoelectric effect.

Photoelectric current increases linearly

with increase in intensity of incident light.

I μA

Intensity (L)

i.e. the number of electrons emitted per second is directly proportional to intensity of light.

Photoelectric current increases with

increase in +ve potential applied to the

anode.

0

Saturation Current L1

L2 L2 > L1 I

μA

+ Potential of A (V)

VS

When all the photoelectrons reach the plate

A, current becomes maximum and is known

as saturation current.

i.e.even in the absence of accelerating

potential, a few photoelectrons manage to

reach the plate on their own due to their

K.E.

When the potential is decreased, the

current decreases but does not become

zero at zero potential.

When –ve potential is applied to the plate A

with respect to cathode, photoelectric

current becomes zero at a particular value of

–ve potential called stopping potential or cut-

off potential.

Intensity of incident light does not affect

the stopping potential.

If Kmax is the maximum kinetic energy of

emitted electron ,

Kmax=e Vo

Saturation Current

1

2

+

I μA

Potential of A (V) 0 VS1

2 > 1

VS2

The saturation current is same for

different frequencies of the incident lights

of same intensity.

Higher the frequency, higher the stopping

potential. i.e. VS α

Variation of stopping potential with frequency of incident radiation

VS

(V)

1

2

ν1

o ν2

o

Stopping potential 0 varies linearly with the frequency of incident radiation

There exists a certain minimum cut-off frequency ν0 for which the stopping potential is zero.

Einstein’s photoelectric equation

Photon energy=work function+ Max.K.E

max.oh h K E

.max

.max

1 2

2

1 1. -

max

h h K Eo

hc hcK E

o

hc hcmv

o

K E hc

o

Photon concept of electromagnetic radiation In interaction of radiation with matter, radiation behaves as if it is made up of particles called photons. Each photon has energy E (=hν) and momentum p (= h ν/c). All photons of light of a particular frequency ν, or wavelength λ, photon energy is independent of intensity of radiation.

Photons are electrically neutral and are not deflected by electric and magnetic fields. In a photon-particle collision , the total energy and total momentum are conserved. However, the number of photons may not be conserved in a collision. The photon may be absorbed or a new photon may be created.

The wave associated with material particles in motion is called matter wave or de Broglie wave.

Dual nature of matter

h h

p mv

Matter wave is neither electromagnetic nor mechanical

Relation between de-Broglie wavelength and kinetic energy of the particle

h 1

2mE mE

h 1

2mqV mqV

oh 12.27A

2meV V

If electron is accelerated through a potential difference of V volt

1.The work function of a metal is the

minimum energy required

1) to remove valence electron from a metal

atom

2) to remove any electron from a metal atom

3) to remove free electron from a metal

surface

4) to remove any electron from a metal

surface

Ans: To remove free electron from a metal surface

2.The work functions of lithium and copper are

2.1 eV and 4.3 eV respectively. Out of these, the

one which is suitable for the photoelectric cell

that works with the visible light is

1) Lithium

2) copper

3) both lithium and copper

4) neither lithium nor copper

Maximum energy of visible energy photon

is about 3.1 eV. Hence visible light can produced photoelectric effect on Lithium but not on Copper

3.A metallic surface has a threshold wave length of

5200Å. This surface is irradiated by monochromatic

light of wavelength 4500Å. Which of the following

statement is true?

1) the electrons are emitted from the surface with

energy between 0 to infinity

2) the electrons are emitted from the surface with

energy between 0 and finite maximum value

3) the electrons are emitted from the surface all

with certain finite energy

4) no electron is emitted from the surface

incident <o

Ans: 2)Photoemission takes place with kinetic varying from zero to maximum

4.Blue light can cause photoelectric

emission from a metal but yellow light

cannot. If red light is incident on the metal

then,

1) photoelectric current will increase

2) rate of emission of photoelectrons will

decrease

3) no photoelectric emission will occur

4) energy of the photoelectrons will

increase

Threshold wavelength is less than that of

yellow light. But wavelength of red is

longer than that of yellow

So the red light cannot cause

photoelectric emission as R > Y > B

Ans: 3)

5. Light of frequency 1.5 times the

threshold frequency is incident on photo

sensitive material. If the frequency is

halved and intensity is doubled, the

photoelectric current becomes

1)quadrupled 2) doubled

3) halved 4) zero

Ans: 4) When frequency is halved, it becomes 0.750. No emission of light takes place (since < 0)

Ans: 4) zero

6. Which of the following radiation will

produce photoelectrons with highest

kinetic energy

1) X-rays 2) gamma rays

3) UV rays 4) visible light

Radiation with highest frequency will liberate electrons with maximum kinetic energy

Ans: 2) Gamma rays

7. The work function of sodium and aluminium is

2eV and 4.2eV respectively. Then

1) Threshold of wavelength of sodium is less

than that of aluminium

2) Threshold of wavelength of sodium is more

than that of aluminium

3) Threshold of wavelength of sodium is equal

to that of aluminium

4) None of the above

sodium alu minium o(sodium) o(alu minium)

1work function

threshold wavlength

If

Ans: 2) Threshold of wavelength of sodium is

more than that of aluminium

8. The graph between and stopping potential (V) for three metals is plotted as shown . Which of the following statement is correct ? 1) Ratio of work functions = 1 : 2 : 4. 2) Ratio of work functions = 4 : 2 : 1. 3) tan is equal to Planck’s constant. 4) The violet colour light can eject photoelectrons from metals 2 and 3

1

1 2 3

1 2 3

1 2 3

1

1 1 1: : : :

: : 1: 2 : 4

o

Ans: 1

9.According to Einstein photoelectric equation slope of plot of the stopping potential of the emitted photo electron verses frequency

1Depends on the intensity of radiation and

metal used

2)Depends on the intensity of radiation

3)Depends on the metal used

4)Independent of metal used and incident

radiation

Ans: (4) always the value of slope is a

constant whose value is equal to plank’s

constant.

10. Relation between stopping potential Vo and maximum velocity of photoelectron v is

o o 2

2

o o

1 11) V 2)V

v v

3) V v 4) V v

Ans: 3

2

o max max max

2

o max

V K.E and K.E v

V v

11.Light of frequency 1.5 times the

threshold frequency produce

photoemission on a metal surface. If the

frequency is halved and intensity is

doubled, the photoelectric current

becomes

1) quadrupled 2) doubled

3) halved 4) zero

When frequency is halved, it becomes 0.750. Since < 0 No emission of light takes place. Ans: 4) zero

12. The photoelectrons emitted from a metal

surface

1) Have the same momentum

2) Have the same kinetic energy

3) Have speeds varying from zero up to a certain

maximum value

4) Are all at rest

Ans: photoelectron can have kinetic varying

from zero to certain maximum value.

Therefore photoelectrons can have speeds

varying from zero up to a certain maximum

value

13. The correct curve stopping potential verses intensity of incident radiation

(X-axis Intensity Y-axis Stopping potential)

2 1 3 4

Stopping potential is independent of intensity.

Ans: (3)

14. The work function of a metal is 2eV . When

a radiation of frequency1.6x1015HZ.is

incident on it ,then

1) There will be photoemission

2)No photoemission

3)There will be photoemission if intensity is

very high

4)There will be photoemission if intensity is

very less

34 15

34 15

19

o

Energyof photon E h 6.63x10 x1.6x10 J

6.63x10 x1.6x106.63eV

1.6x10

h

Ans: There will be photoemission

15. A photon of energy 8 eV is incident on

a metal surface of threshold frequency

1.6 1015 Hz. The K. E. of the photo

electrons emitted (in eV), (h = 6 10–34 Js)

1) 1.8 2) 6

3) 2 4) 1.2

34 15

o 19

6 10 1.6 10work function h 6eV

1.6 10

Emax = 8 – 6 = 2 eV

16. Maximum velocity of photoelectron from a surface is 1.2 106 ms– 1. Assuming the specific charge of electron to be 1.8 1011 Ckg– 1 ,the value of stopping potential in volt will be

1) 4V 2) 6V

3) 2V 4) 3 V

2

max 0

2 6 2

maxo 11

1mv eV

2

v1 1 (1.2x10 )V x 4

e2 2 1.8x10m

Ans: 1) 4 V

17. When a metal surface is illuminated with a

monochromatic radiation of wavelength λ the

stopping potential is 3V. When it is illuminated

with radiation of wavelength 2λ,stopping

potential reduces to V. Threshold wavelength

for the metal is

1) 8 λ 2) 6 λ

3) 4 λ 4) 4 λ/3

hc hcK.E= -λ λ

ohc hc3Ve= - .........(1)λ λ

ohc hcVe= - ...........(2)2λ λ

o4

o

Ans:(3)

1 1 2 2

2 1

K λ K λ1)

λ λ

1 1 2 2

2 1

K λ K λ2)

λ λ

1 2 2 1

2 1

K λ K λ3)

λ λ

1 2 2 1

2 1

K λ K λ4)

λ λ

18. The kinetic energies of photoelectrons

emitted from a metal are K1 and K2 when it is

irradiated with lights of wavelength 1 and 2

respectively. The work function of the metal is

1 1 1 1

1

2 2 2 2

2

2 2 2 1 1 1

2 1 1 1 2 2

h cW + K h c W λ + K λ ......................(1)

λ

h cW + K h c W λ + K λ .....................(2)

λ

From (1) and (2) W λ + K λ W λ + K λ

or W λ W λ K λ K λ

W

1 1 2 2

2 1

K λ K λ

λ λ

Answer: (1)

19. When ultraviolet light is incident on a photocell, its stopping potential is Vo and the maximum momentum of electron is Po .When X-ray is incident on the same cell

1) Both Vo and Po will increase.

2) Both Vo and Po will decrease

3) Vo increase and Po will decrease

4) Vo remain same and Po will increase.

Energy of X-ray photon is greater than ultraviolet photon Therefore Kinetic energy of emitted electron and stopping potential w ill be more for ultraviolet light In turn the momentum of the emitted electron

Ans: 1)Both Vo and Po will increase.

20. In an experiment with photoelectric effect,

the slope of stopping potential verses frequency

of incident light is found to be 4.130x10-15 Vs.

The value of plank’s constant from the graph is

1)6.591x10-34Js 3) 6.616x10-34Js

2)3 6.650x10-34Js 4) 6.631x10-34Js

Slope of Vo verses = h/e

h =slope x e=4.130x10-15 x1.6x10-19

=6.616x10-34

Ans: (2)

21. When a monochromatic point source of light at

a distance of 0.2m from a photocell. The cut off

voltage and saturation current is 0.6V and 18mA. If

the same source is placed 0.6m away from the cell,

the cut off voltage and saturation current is

1) 0.2V and 2mA 2) 1.8V and 6mA

3) 0.6V and 6mA 4) 0.6V and 2mA

As the source is moved away ,the intensity of light falling on the surface reduces according to the relation

2

1intensity α

distance

Therefore when the distance is increased by 3 times intensity reduces by 9 time and hence the current reduces to 2mA Frequency remains same and hence the cut off voltage remains same (0.6V)

Ans: 4) 0.6V and 2mA

22. The maximum kinetic energy of photoelectrons is 1eV and 3eV for incident photon frequency and respectively. Maximum kinetic energy of photoelectrons for the incident frequency

3

2

9

4

1) 8eV 2) 6eV

3) 45eV 4) 3eV

1

1

1

1

1

1

1

Let Energyof light freuency E ;

3 3Energyof light freuency E

2 2

9 9Energyof light freuency E

4 4

From Einstein 'sequation

1 E

E 4, 333 E

2

9K.E E 6eV

4

Ans: 2) 6eV

23. A photosensitive metal is first incident with

the radiation of wavelength 400 nm and then with

radiations of wavelength 800 nm. The change in

the maximum kinetic energy of the photoelectron

is

1) 0.55 eV 2) 1.55 eV

3) 2.0 eV 4) 1.0 eV

1 2

26

7 7

1 1E hc

1 120x10

4x10 8x10

1.56eV

Ans: (2)

24. Maximum velocity of photoelectrons emitted

by a photo emitter is 2X106 m/s. If e/m=1.8X1011

for electrons, the stopping potential of the

emitter is

1) 11.1V 2) 20V

3) 40V 4) 2V

2

max 0

2 6 2

maxo 11

1mv eV

2

v1 1 (2x10 )V x 11.1V

e2 2 1.8x10m

Ans: 2) 11.1V

25. Light photons of energies 1 eV and 2.5 eV

are successively incident on a metal surface of

work function 0.5 eV , then the ratio maximum

velocities of the emitted photo-electrons will be

1) 1 : 5 2) 1 : 4

3) 1 : 3 4) 1 : 2

26. When UV light of wavelength 100 nm is

incident on a silver surface of work function

4.7eV, a negative potential of 7.7V is required to

stop the photo-electrons from reaching the

collector plate. The potential which is required

to stop the photoelectrons when light of

wavelength 200 nm is incident on it will be

1) 1.5V 2) 3V

3) 4.5V 4) 6V

E = 7.7 eV, W=4.7eVK1

Energy of photon: E = W + E1 K1

= 4.7 + 7.7

= 12.4 eV

E λ 100 nm 12 1= = = E λ 200 nm 2

1 2E

1 E = 6.22 2

eV

2 : : 6.2 2

- 6.2 - 4.7 1.5 2 2

1.5

nd case Energy of photon E eV

E E W eVK

Hence the stopping potential is V

Ans:1

27. The ratio of linear momentum of an electron and alpha particle when both are accelerated through a potential difference of 100 volt

2 e

a

m

m3) e

a

m

m4)

2

e

a

m

m

1) 1 2)

1& 2

2

e

e e e e

p mq q q

p m q m

p m q m

: 4)2

e

a

mAns

m

28. An X-ray tube operates at 10kV. The ratio of X-ray wavelength to that of de-Broglie is 1)10:1 2) 1:10 3) 1:100 4) 100:1

2

210

: 10 :1

d

x

d

x

d x

hde Broglie wavelength

meV

hcWavelengthof X ray

eV

mc

eV

Ans: 1)10:1

29. If the kinetic energy of the particle is increased by 16 times ,the percentage change in the de-Broglie wavelength is 1)25% 2)75% 3)60% 4)50%

2 1 1

1 2 1

2 1 1

1

1

16 4

10.25

4

0.75 75%

E

E E

E E

changein wavelength or

Ans: 2)75%

30. The de-Broglie wavelength associated with

proton changes by 0.25% if its momentum

changes by p. The initial momentum is

1) 100 p 2) p/400

3) 401 p 4) p/100

(1)

0.251 (2)

100

401

h

p

h

p p

solving aboveequations p p

Ans: 3) 401 p

31. The de-Broglie wavelength of electron in ground state of hydrogen atom is

1) 0.5 2)1.06 3) 1.67 4)3.33A A A Ao o o o

The circumference of ground state orbit is equal to the wavelength of corresponding de-Broglie wave i.e.

o

o

o

2 r ( 0.53A)

3.33A

or

:4)3.33Ao

Ans

32. The maximum kinetic energy of photoelectrons from the surface of silver of threshold wavelength λo due to a radiation of wavelength λ (λ< λo ) is given by

1) ( )ohc 0

2)( )

hc

1 13)

o

hc

4) o

o

hc

max.

o

o

o

hc hcK E

hc

Ans: (4)

33. Of the following the graph which represents the

variation of momentum (p) of a particle with the

wavelength () of matter wave is

p

p

p

p

1h

p p

Hence the plot is a rectangular hyperbola Ans:3

34.If the velocity of a particle is reduced to

one-third then the percentage increase in its

de-Broglie wavelength is

1) 50% 2) 100%

3) 200% 4) 300%

h h hλ = and λ' = = 3 = 3λ

vm v m vm

3

Change in de - Broglie wavelength = 2λ

2λPercentage change = ×100% = 200%

λ

Answer is (3)

35. The ratio of de-Broglie wavelength associated with proton and particle accelerated through same potential difference

1) 1 2)2 3) 8

14)

8

p

α

p

α

h 1For a charged particle : λ =

2 m q V m q

1For a proton : λ

m e

1 1For α - particle : λ =

(4m) (2e) 8 m e

λ 8 m e= = 8

λ m e

Answer is (3)

36. If the momentum of two particles of

mass m and 2m are equal, then the ratio of

wavelength of the matter wave is

1) 1 : 2 2) 2 : 1

3) 1 : 1 4) 1 : 3

1 2

2 1';

h p1

p p

1 : 2 = 1 : 1

Ans: (3)

37. An X–ray photon has a wavelength of 0.02 Å. Its momentum is 1) 3.3 10– 22 kg m/s 2) 6.6 10– 21 kg m/s 3) 6.6 10– 24 kg m/s 4) 1.65 1022 kg m/s

Answer: (1)

-34 -34

-10 -12

-22

hMomentum: p=

λ

6.6×10 6.6×10 = =

0.02×10 2×10

=3.3×10

38. If E is the energy, de-Broglie wavelength is proportional to 1) E–1 for both photons and particles 2) E–1 for photons and E–1/2 particles 3) E–1/2 for both photons and particles 4) E–1/2 for photons and E–1 for particles

h cFor photon: E =

λ1 1λ λ EE

hFor a particle: λ=

2mE

1 1 2 λ λ E

E

Answer is (2)

39. For given kinetic energy which of the following has the longest de-Broglie wavelength?

1) Electron 2)Proton

3)Neutron 4) alpha particle

e p n e p n α

h 1λ = or λ ,

2mE m

> (m < m < m < m )

Answer: (1)

40. Electrons used in an EM are accelerated by a voltage of 25kV. If the voltage is increased to 100kV then the de-Broglie wavelength associated with the electrons would

1) Increases to 2 times 2) increases to 4 times 3)decreases by 2 times 4)decreases by 4 times

Vλ25 kV1 112λ

V 100 kVλ 2V 21

λ1λ

2 2

Ans: 3