CBSE Class 12 Physics Dual Nature of Radiation and Matter MCQs Set 06

Question: A proton and an a-particle are accelerated through the same potential difference. The ratio of de Broglie wavelength lp to that of la is
(a) 2 : 1
(b) 4 : 1
(c) 6 : 1
(d) 8 : 1
Answer: d

Question: When the velocity of an electron increases, its de Broglie wavelength
(a) increases
(b) decreases
(c) remains same
(d) may increase or decrease 
Answer: b

Question: The wavelength of matter wave is independent of
(a) mass
(b) velocity
(c) momentum
(d) charge 
Answer: d

Question: If the momentum of an electron is changed by p, then the de Broglie wavelength associated with it changes by 0.5%. The initial momentum of electron will be
(a) 200p
(b) 400p
(c) p/ 200
(d) 100p 
Answer: a

Question: The phenomenon of photoelectric emission was discovered in 1887 by
(a) Albert Einstein
(b) Heinrich Hertz
(c) Wilhelm Hallwachs
(d) Philipp Lenard 
Answer: b

 Question:The de Broglie wavelength of a particle of kinetic energy K is l. What will be the wavelength of the particle, if its kinetic energy is K/4 ?
(a) λ
(b) 2λ
(c) λ/2
(d) 4λ 
Answer: b

Question: The de Broglie wavelength associated with a ball of mass 150 g travelling at 30 m s^–1 is
(a) 1.47 × 10^–34 m
(b) 1.47 × 10^–16 m
(c) 1.47 × 10^–19 m
(d) 1.47 × 10^–31 m 
Answer: a

 Question: A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to 
(a) H
(b) H 1/2
(c) H0
(d) H–1/2 
Answer: d

Question: The threshold frequency of a certain metal is 3.3 × 1014 Hz. If light of frequency 8.2 × 1024 Hz is incident on the metal, then the cut off voltage for photoelectric emission is
(Given h = 6.63 × 10–34 J s)
(a) 2 V
(b) 4 V
(c) 6 V
(d) 8 V
Answer: a

Question: Who established that electric charge is quantised ?
(a) J.J. Thomson
(b) William Crookes
(c) R.A Millikan
(d) Wilhelm Rontgen 
Answer: c

Question: If alpha particle, proton and electron move with the same momentum, then their respective de Broglie wavelengths la, lp, le are related as
(a) λa = λp =λe
(b) λa < λp < λe
(c) λa > λp > le
(d) λp > λe >λa 
Answer: a

Question: The de Broglie wavelength of an electron in a metal at 27°C is (Given m_e = 9.1 × 10^–31 kg, k_B = 1.38 × 10^–23 J K^–1)
(a) 6.2 × 10^–9 m
(b) 6.2 × 10^–10 m
(c) 6.2 × 10^–8 m
(d) 6.2 × 10^–7 m 
Answer: a

Question: Photons absorbed in matter are converted to heat. A source emitting n photons per second of frequency u is used to convert 1 kg of ice at 0°C to water at 0°C. Then, the time T taken for the conversion
(a) decreases with increasing n, with u fixed.
(b) decreases with n fixed, u increasing.
(c) remains constant with n and u changing such that nu = constant.
(d) All of these.
Answer: d

Question: The maximum frequency and minimum wavelength of X-rays produced by 30 kV electrons respectively is
(a) 7.24 × 1018 Hz, 0.041 nm
(b) 3.21 × 1018 Hz, 0.211 nm
(c) 5.32 × 1018 Hz, 0.001 nm
(d) 2.13 × 1018 Hz, 0.011 nm 
Answer: a

Question: A student performs an experiment on photoelectric effect using two materials A and B. A plot of stopping potential (V₀)vs frequency (u) (V₀) frequency is as shown in the figure. image 15
The value of h obtained from the experiment for both A and B respectively is (Given electric charge of an electron = 1.6 × 10^–19 C)
(a) 3.2 × 10^–34 J s, 4 × 10^–34J s
(b) 6.4 × 10^–344 J s, 8 × 10^–34 J s
(c) 1.2 × 10^–34 J s, 3.2 × 10^–34 J s
(d) 4.2 × 10^–34 J s, 5 × 10^–34 J s 
Answer: b

Question: The minimum energy required for the electron emission from the metal surface can be supplied to the free electrons by which of the following physical processes?
(a) Thermionic emission
(b) Field emission
(c) Photoelectric emission
(d) All of these
Answer: d

Question: Assume that a molecule is moving with the root mean square speed at temperature 300 K.
The de Broglie wavelength of nitrogen molecule is (Atomic mass of nitrogen = 14.0076 u,
h = 6.63 × 10–³⁴ J s, k_B = 1.38 × 10^–23 J ^K–1, 1 u = 1.66 × 10^–27 kg)
(a) 2.75 × 10^–11 m
(b) 2.75 × 10^–12 m
(c) 3.24 × 10^–11 m
(d) 3.24 × 10^–12 m 
Answer: a

Assertion & Reasoning Based MCQs

two statements are given-one labelled Assertion (A) and the other labelled Reason (R).
Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false 

Question: Assertion (A) : The de-Broglie wavelength of particle having kinetic energy K is λ. If its kinetic energy becomes 4 K then its new wavelength would be λ/2.
Reason (R) : The de-Broglie wavelength λ is inversely proportional to square root of the kinetic energy. 

Answer: a

Question: Assertion (A) : Photoelectric effect demonstrates the wave nature of light.
Reason (R) : The number of photoelectrons is proportional to the frequency of light.

Answer: d

Question: Assertion (A) : A photon has no rest mass, yet it carries definite momentum.
Reason (R) : Momentum of photon is due to its energy and hence its equivalent mass.

Answer: a

Question: Assertion (A) : There is a physical significance of matter waves.
Reason (R) : Both interference and diffraction occurs in it. 

Answer: a

Question: Assertion (A) : Photosensitivity of a metal is high if its work function is small.
Reason (R) : Work function = hu0, where u0 is the threshold frequency

Answer: b

Very Short Answer Type Questions

Question: Do all the electrons that absorb a photon come out as photoelectron?
Answer : Not all the electrons that absorb a photon come out as photoelectrons because most of electrons get scattered into the metal. Only those electrons come out as photoelectrons whose energy becomes greater than work function of metal.

Question: If light of wavelength 412.5 nm is incident on each of the metals given in table, which one will show photoelectric emission and why? Metal Work Function (eV) 3 IMAGE
Answer : Wavelength of incident light, λ = 412.5 nm Energy of incident light, E hc /λ =1242eV nm nm/412. 5. nm= 3 eV Metals Na and K will show photoelectric emission because their work functions are less than the energy of incident light.

Question: The threshold wavelength for two photosensitive surfaces A and B areλ1 and λ2 respectively. What is the ratio of the work functions of the two surfaces?
Answer : Work function=hν=hC/λ ∴The ratio, Φ_A/Φ_B=hC/λ_AXλ_B/hC=λ₂/λ₁

Question: Write the relationship of de-Broglie wavelength l associated with a particle of mass m in terms of its kinetic energy E.
Answer : λ = h/√2mE

Short Answer Type Questions 

Question: A light beam of wavelength 400 nm is incident on a metal plate of work function of 2.2 eV. An electron absorbs a photon and makes some collisions before coming out of the metal.
Assuming that 10% of the instantaneous energy is lost to the metal in each collision.
(i) Find the kinetic energy of electron which makes two collisions as it comes out of the metal.
(ii) Under the same assumptions, find the minimum number of collisions the electron can suffer before it becomes unable to come out of metal.
(Use hc = 12400 eV Å)
Answer : 16 E λ = Energy of the photon = hc/= 1 .24 ×10⁴/4000 eV = 3.1 eV
(i) K.E. of emitted e– = (3.1 × (0.9)² – 2.2) eV = 0.31 eV
(ii) For e– not be able to come out, its energy should be less
than 2.2 eV
i.e., (3.1) × (0.9)ⁿ < 2.2, n > 4

Case Based MCQs

Photoelectric Effect Photoelectric effect is the phenomenon of emission of electrons from a metal surface, when radiations of suitable frequency fall on them. The emitted electrons are called photoelectrons and the current so produced is called photoelectric current. 

Question: It is observed that photoelectron emission stops at a certain time t after the light source is switched on. The stopping potential (V) can be represented as
(a) 2(KE_max/e)
(b) (KE_max/e)
(c) (KE_max/3e)
(d) (KE_max/2e) 
Answer: b

Question: A point source of light of power 3.2 × 10^–3 W emits monoenergetic photons of energy 5.0 eV and work function 3.0 eV. The efficiency of photoelectron emission is 1 for every 10⁶ incident photons. Assume that photoelectrons are instantaneously swept away after emission.
The maximum kinetic energy of photon is
(a) 4 eV
(b) 5 eV
(c) 2 eV
(d) Zero 
Answer: c

Question: With the increase of intensity of incident radiations on photoelectrons emitted by a photo tube, the number of photoelectrons emitted per unit time is
(a) increases
(b) decreases
(c) remains same
(d) none of these 
Answer: a

Question: If the frequency of incident light falling on a photosensitive metal is doubled, the kinetic energy of the emitted photoelectron is
(a) unchanged
(b) halved
(c) doubled
(d) more than twice its initial value
Answer: d