Question 1

Match List I with List II : List I List II A. E = h I. de Broglie wavelength B. Diffraction and Interference II. Particle nature of light C. = h/p III. Wave nature of light D. Compton effect IV. Energ

Accepted Answer

The relation E = h represents the energy of a photon, which corresponds to IV. Diffraction and interference are phenomena that can only be explained by considering light as a wave, which corresponds to the wave nature of light (III). The relation = h/p gives the de Broglie wavelength of a particle, which corresponds to I. The Compton effect involves the scattering of a photon by a charged particle, demonstrating the particle nature of light, which corresponds to II. The correct matching is A-IV,

Question 2

A beam of light falls on a metal surface such that photo-electrons are generated. If power of the light source starts to decrease linearly with time t, then variation of the photocurrent I and magnitu

Accepted Answer

The power of the incident light is P = n h , where n is the number of photons incident per unit time and is the frequency. As the power decreases linearly with time, the number of incident photons n also decreases linearly, assuming the frequency remains constant. The photocurrent I is directly proportional to the number of incident photons per unit time (I n). Thus, the photocurrent I decreases linearly with time. The stopping potential V is given by Einstein's photoelectric equation e|V| = h -

Question 3

A photon and an electron, each of 20 eV energy, move in free space. The ratio of linear momentum of electron p_e to that of photon p_ Ph , p_e p_ Ph is : (Take speed of light =3 10^8 ms^ -1 , charge o

Accepted Answer

For a photon, the energy E and linear momentum p_ Ph are related by: p_ Ph = E c For an electron, the kinetic energy E and linear momentum p_e are related by: p_e = 2mE The ratio of the linear momentum of the electron to that of the photon is: p_e p_ Ph = 2mE E c = c 2m E Given: E = 20 eV = 20 1.6 10^ -19 J = 32 10^ -19 J m = 9 10^ -31 kg c = 3 10^8 m/s Substituting the values into the ratio: p_e p_ Ph = 3 10^8 2 9 10^ -31 32 10^ -19 p_e p_ Ph = 3 10^8 18 10^ -31 32 10^ -19 p_e p_ Ph = 3 10^8 9

Question 4

For a metal of work function 6.6 eV, which of the following wavelengths of incident radiation does not give rise to the photoelectric effect ? (Take Planck's constant as 6.6 10^ -34 J s)

Accepted Answer

The threshold wavelength _0 is given by _0 = hc . Substituting the given values: _0 = 6.6 10^ -34 3 10^8 6.6 1.6 10^ -19 _0 = 3 1.6 10^ -7 m _0 = 1.875 10^ -7 m = 187.5 nm For the photoelectric effect to take place, the wavelength of incident radiation must be less than or equal to the threshold wavelength ( _0). Among the given options, 200 nm is greater than 187.5 nm. Thus, radiation of wavelength 200 nm will not give rise to the photoelectric effect. Answer: 200 nm

Question 5

A ray of light with wavelength is incident on three different photo-electric cells namely 1, 2 and 3. The threshold wavelength of these photo-electric cells are _1, _2, and _3, respectively and the ma

Accepted Answer

According to Einstein's photoelectric equation, the magnitude of the stopping potential V is given by: eV = hc - hc _ th For photoelectric emission to take place, the incident wavelength must be less than the threshold wavelength _ th . For cell 1, > _1. No photoelectric emission occurs, so V_1 = 0. For cell 2, 0. For cell 3, _3. Photoelectric emission occurs, and V_3 = hc e ( 1 - 1 _3 ) > 0. Since _3 and _2 > , it follows that _3 > _2, which gives 1 _3 Therefore, 1 - 1 _3 > 1 - 1 _2 , which imp

Question 6

A photon and an electron (mass m ) have the same energy E. The ratio ( _ photon / _ electron ) of their de Broglie wavelengths is: (c is the speed of light)

Accepted Answer

Photon & electron have same energy E _ photon _ electron = h c E h 2 mE =c 2 ~m E

Question 7

Which of the following options represent the variation of photoelectric current with property of light shown on the x -axis?

Accepted Answer

i intensity so curve A is correct Photo current does not depend linearly frequency, so graph C & D are not correct.

Question 8

If c is the velocity of light in free space, the correct statements about photon among the following are: A. The energy of a photon is E=h v. B. The velocity of a photon is c. C. The momentum of a pho

Accepted Answer

(A) If c is the velocity of light so, E=h (Energy of photon) (B) Velocity of photon is equal to velocity of light i.e. c. (C) = h p aligned & p= h \ & p= h c aligned (D) In photon-electron collision both total energy and total momentum are conserved.

Question 9

If is the work function of photosensitive material in eV and light of wavelength of numerical value = h c e metre, is incident on it with energy above its threshold value at an instant then the maximu

Accepted Answer

( K . E )_ = h c - _0 and = h c e ( K . E )_ = h c h c e - _0 (K . E)_ =e- _0 (K . E .)_ =e

Question 10

An electron and an alpha particle are accelerated by the same potential difference. Let _ and _a denote the de-Broglie wavelengths of the electron and the alpha particle, respectively, then:

Accepted Answer

de-Broglie wavelength is given by = h p = h 2 m q V For same potential difference 1 m q _ _e = m_e q_e m_ q_ m_ m_e _e _

Question 11

The graph which shows the variation of ( 1 ^2 ) and its kinetic energy, E is (where is de Broglie wavelength of a free particle):

Accepted Answer

de-Broglie wavelength = h P = h m v = h 2 m E where E= 1 2 m v^2 Squaring both sides, aligned & ^2= h^2 4 m^2 E \ & 1 ^2 = (constant) E aligned Graph passes through origin with constant slope.

Dual Nature of Matter — Previous Year Questions & Solutions