JEE Physics Dual Nature Of Radiation And Matter MCQs Set 06

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Chapter-wise Objective Questions: Dual Nature Of Radiation and Matter

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Multiple Choice Questions

Question 1: A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be
(a) 1840 keV
(b) 1/1840 keV
(c) 1 keV
(d) 920 keV
Show Answer & Explanation

Answer: (c) 1 keV

Explanation:
1. \( K=qV=1 \) keV, independent of the mass.

Teacher's Note:
1. Energy gained is qV.

Question 2: If an electron and a photon propagate with the same wavelength, they have the same
(a) Energy
(b) Momentum
(c) Velocity
(d) Angular momentum
Show Answer & Explanation

Answer: (b) Momentum

Explanation:
1. \( p=h/\lambda \) for both.

Teacher's Note:
1. Same wavelength, same momentum.

Question 3: According to de Broglie, the wavelength of an electron in the second orbit is \( 10^{-9} \) m. The circumference of the orbit is
(a) \( 10^{-9}\ \text{m} \)
(b) \( 2\times10^{-9}\ \text{m} \)
(c) \( 3\times10^{-9}\ \text{m} \)
(d) \( 4\times10^{-9}\ \text{m} \)
Show Answer & Explanation

Answer: (b) \( 2\times10^{-9}\ \text{m} \)

Explanation:
1. \( 2\pi r=n\lambda=2\times10^{-9} \) m.

Teacher's Note:
1. Circumference = n lambda.

Question 4: If the mass of a microscopic particle as well as its speed are halved, the de Broglie wavelength
(a) Increases by a factor more than 2
(b) Increases by a factor of 2
(c) Decreases by a factor of 2
(d) Decreases by a factor more than 2
Show Answer & Explanation

Answer: (a) Increases by a factor more than 2

Explanation:
1. Momentum becomes one quarter, so \( \lambda \) becomes four times.

Teacher's Note:
1. 4 is more than 2.

Question 5: An electron and a proton are accelerated through the same potential. The ratio \( \lambda_e/\lambda_p \) is
(a) 1
(b) \( m_e/m_p \)
(c) \( m_p/m_e \)
(d) \( \sqrt{m_p/m_e} \)
Show Answer & Explanation

Answer: (d) \( \sqrt{m_p/m_e} \)

Explanation:
1. \( \lambda\propto1/\sqrt m \) for equal charge and voltage.

Teacher's Note:
1. Lighter has the longer wavelength.

Question 6: An electron, a proton and an alpha particle have the same kinetic energy. The de Broglie wavelengths satisfy
(a) \( \lambda_e>\lambda_p>\lambda_\alpha \)
(b) \( \lambda_p>\lambda_e>\lambda_\alpha \)
(c) \( \lambda_\alpha>\lambda_e>\lambda_p \)
(d) \( \lambda_\alpha>\lambda_p>\lambda_e \)
Show Answer & Explanation

Answer: (a) \( \lambda_e>\lambda_p>\lambda_\alpha \)

Explanation:
1. \( \lambda\propto1/\sqrt m \) at equal K.

Teacher's Note:
1. Heavier means shorter wavelength.

Question 7: The de Broglie wavelength of an electron with kinetic energy 120 eV is (h = 6.63e-34 J s, m = 9.11e-31 kg, e = 1.6e-19 C)
(a) 725 pm
(b) 500 pm
(c) 322 pm
(d) 112 pm
Show Answer & Explanation

Answer: (d) 112 pm

Explanation:
1. \( \lambda=1.227/\sqrt{120}\ \text{nm}=0.112 \) nm = 112 pm.

Teacher's Note:
1. 12.27 / sqrt(V) in Å.

Question 8: If \( \lambda_p \) and \( \lambda_\alpha \) are the wavelengths of protons and alpha particles of equal kinetic energies, then
(a) \( \lambda_p=\lambda_\alpha/4 \)
(b) \( \lambda_p=\lambda_\alpha/2 \)
(c) \( \lambda_p=\lambda_\alpha \)
(d) \( \lambda_p=2\lambda_\alpha \)
Show Answer & Explanation

Answer: (d) \( \lambda_p=2\lambda_\alpha \)

Explanation:
1. \( \lambda\propto1/\sqrt m \) and \( m_\alpha=4m_p \), so \( \lambda_p=2\lambda_\alpha \).

Teacher's Note:
1. Mass ratio 4 gives wavelength ratio 2.

Question 9: Radiation emitted when an electron in hydrogen jumps from the first excited state to the ground state irradiates a photosensitive material. The stopping potential is 3.57 V. The threshold frequency of the material is
(a) \( 1.6\times10^{15}\ \text{Hz} \)
(b) \( 2.5\times10^{15}\ \text{Hz} \)
(c) \( 4\times10^{15}\ \text{Hz} \)
(d) \( 5\times10^{15}\ \text{Hz} \)
Show Answer & Explanation

Answer: (a) \( 1.6\times10^{15}\ \text{Hz} \)

Explanation:
1. \( E=10.2 \) eV, \( \phi=10.2-3.57=6.63 \) eV.
2. \( \nu_0=\phi/h=1.6\times10^{15} \) Hz.

Teacher's Note:
1. Lyman alpha energy.

Question 10: A 200 W sodium street lamp emits yellow light of wavelength 0.6 μm and is 25% efficient in converting electrical energy to light. The number of photons emitted per second is
(a) \( 62\times10^{20} \)
(b) \( 3\times10^{19} \)
(c) \( 1.5\times10^{20} \)
(d) \( 6\times10^{18} \)
Show Answer & Explanation

Answer: (c) \( 1.5\times10^{20} \)

Explanation:
1. Light power = 50 W; photon energy = \( hc/\lambda=3.3\times10^{-19} \) J.
2. \( N=50/3.3\times10^{-19}=1.5\times10^{20} \).

Teacher's Note:
1. 25 percent of 200 W is 50 W.

Question 11: An alpha particle moves in a circular path of radius 0.83 cm in a magnetic field of 0.25 Wb/m2. Its de Broglie wavelength is
(a) 10 Å
(b) 0.1 Å
(c) 1 Å
(d) 0.01 Å
Show Answer & Explanation

Answer: (d) 0.01 Å

Explanation:
1. \( p=qBr=2\times1.6\times10^{-19}\times0.25\times0.83\times10^{-2}=6.6\times10^{-22} \).
2. \( \lambda=h/p=10^{-12} \) m = 0.01 Å.

Teacher's Note:
1. p = q B r.

Question 12: If the momentum of an electron is changed by P, then the de Broglie wavelength changes by 0.5%. The initial momentum of the electron was
(a) \( P/200 \)
(b) 100 P
(c) 200 P
(d) 400 P
Show Answer & Explanation

Answer: (c) 200 P

Explanation:
1. \( \lambda\propto1/p \), so \( \Delta p/p=0.5\% \) and \( p=200P \).

Teacher's Note:
1. Small fractional changes are equal in magnitude.

Question 13: A photon of frequency \( 1\times10^{14} \) s-1 is incident on a metal of threshold frequency \( 5\times10^{13} \) s-1. The kinetic energy of the ejected electron is
(a) \( 3.3\times10^{-21}\ \text{J} \)
(b) \( 6.6\times10^{-21}\ \text{J} \)
(c) \( 3.3\times10^{-20}\ \text{J} \)
(d) \( 6.6\times10^{-20}\ \text{J} \)
Show Answer & Explanation

Answer: (c) \( 3.3\times10^{-20}\ \text{J} \)

Explanation:
1. \( K=h(\nu-\nu_0)=6.63\times10^{-34}\times5\times10^{13}=3.3\times10^{-20} \) J.

Teacher's Note:
1. K = h (nu - nu0).

Question 14: For photoelectric emission from a certain metal the cutoff frequency is ν. If radiation of frequency 2ν impinges on the metal plate, the maximum possible velocity of the emitted electron will be
(a) \( 2\sqrt{h\nu/m} \)
(b) \( \sqrt{h\nu/2m} \)
(c) \( \sqrt{h\nu/m} \)
(d) \( \sqrt{2h\nu/m} \)
Show Answer & Explanation

Answer: (d) \( \sqrt{2h\nu/m} \)

Explanation:
1. \( K=2h\nu-h\nu=h\nu \), so \( v=\sqrt{2h\nu/m} \).

Teacher's Note:
1. K = h nu.

Question 15: The wavelength of an electron and of a photon of the same energy E are related by
(a) \( \lambda_p\propto1/\sqrt{\lambda_e} \)
(b) \( \lambda_p\propto\lambda_e^2 \)
(c) \( \lambda_p\propto\lambda_e \)
(d) \( \lambda_p\propto\sqrt{\lambda_e} \)
Show Answer & Explanation

Answer: (b) \( \lambda_p\propto\lambda_e^2 \)

Explanation:
1. \( \lambda_e=h/\sqrt{2mE} \) and \( \lambda_p=hc/E \), so \( \lambda_p\propto\lambda_e^{2} \).

Teacher's Note:
1. Eliminate E.

Question 16: The velocity of a particle is 3 times that of an electron and the ratio of their de Broglie wavelengths (particle to electron) is \( 1.814\times10^{-4} \). The particle is
(a) Neutron
(b) Deuteron
(c) Alpha
(d) Tritium
Show Answer & Explanation

Answer: (a) Neutron

Explanation:
1. \( \lambda\propto1/mv \), so \( m_p=m_e/(3\times1.814\times10^{-4})\approx1837m_e \).
2. This is the mass of a neutron.

Teacher's Note:
1. Compare with 1840 electron masses.

Question 17: Light with an energy flux of 25 x 10^4 W/m2 falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm2, the average force exerted on the surface is
(a) 1.25 x 10^-6 N
(b) 2.50 x 10^-6 N
(c) 1.20 x 10^-6 N
(d) 3.0 x 10^-6 N
Show Answer & Explanation

Answer: (b) 2.50 x 10^-6 N

Explanation:
1. \( F=2IA/c=2\times25\times10^{4}\times15\times10^{-4}/3\times10^{8}=2.5\times10^{-6} \) N.

Teacher's Note:
1. Reflection doubles the momentum transfer.

Question 18: When the energy of the incident radiation is increased by 20%, the kinetic energy of the photoelectrons increases from 0.5 eV to 0.8 eV. The work function is
(a) 0.65 eV
(b) 1.0 eV
(c) 1.3 eV
(d) 1.5 eV
Show Answer & Explanation

Answer: (b) 1.0 eV

Explanation:
1. \( 1.2(0.5+\phi)=0.8+\phi \) gives \( \phi=1.0 \) eV.

Teacher's Note:
1. Set up two equations.

Question 19: If the kinetic energy of a particle is increased to 16 times its previous value, the percentage change in the de Broglie wavelength is
(a) 25
(b) 75
(c) 60
(d) 50
Show Answer & Explanation

Answer: (b) 75

Explanation:
1. \( \lambda\propto1/\sqrt K \), so \( \lambda'=\lambda/4 \), a 75 percent decrease.

Teacher's Note:
1. Fall of 3/4.

Question 20: A metallic surface is illuminated with monochromatic light of wavelength λ. The stopping potential is 3V0. With wavelength 2λ it is V0. The threshold wavelength is
(a) \( 4\lambda \)
(b) \( \lambda/4 \)
(c) \( \lambda/6 \)
(d) \( 6\lambda \)
Show Answer & Explanation

Answer: (a) \( 4\lambda \)

Explanation:
1. \( hc/\lambda=\phi+3eV_0 \) and \( hc/2\lambda=\phi+eV_0 \) give \( eV_0=hc/4\lambda \) and \( \phi=hc/4\lambda \).
2. So \( \lambda_0=4\lambda \).

Teacher's Note:
1. Subtract the two equations.

Question 21: A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is
(a) \( 2E/c \)
(b) \( 2E/c^2 \)
(c) \( E/c^2 \)
(d) \( E/c \)
Show Answer & Explanation

Answer: (a) \( 2E/c \)

Explanation:
1. Incident momentum \( E/c \) is reversed, so the change is \( 2E/c \).

Teacher's Note:
1. Reflection means 2p.

Question 22: Light of wavelength 500 nm is incident on a metal with work function 2.28 eV. The de Broglie wavelength of the emitted electron is
(a) \( \le 2.8\times10^{-12}\ \text{m} \)
(b) \( <2.8\times10^{-10}\ \text{m} \)
(c) \( <2.8\times10^{-9}\ \text{m} \)
(d) \( \ge 2.8\times10^{-9}\ \text{m} \)
Show Answer & Explanation

Answer: (d) \( \ge 2.8\times10^{-9}\ \text{m} \)

Explanation:
1. \( K_{max}=2.48-2.28=0.2 \) eV, so \( \lambda\ge12.27/\sqrt{0.2}=27.4 \) Å \( =2.74\times10^{-9} \) m.
2. Slower electrons have a longer wavelength.

Teacher's Note:
1. The maximum KE gives the minimum wavelength.

Question 23: A surface is illuminated with light of wavelength λ and then λ/2. The maximum kinetic energy in the second case is 3 times that in the first. The work function of the material is
(a) \( hc/3\lambda \)
(b) \( hc/2\lambda \)
(c) \( hc/\lambda \)
(d) \( 2hc/\lambda \)
Show Answer & Explanation

Answer: (b) \( hc/2\lambda \)

Explanation:
1. \( 2hc/\lambda-\phi=3(hc/\lambda-\phi) \) gives \( \phi=hc/2\lambda \).

Teacher's Note:
1. Two equations.

Question 24: The threshold frequency of a photosensitive metal is 7 x 10^13 Hz. If light of frequency 10^14 Hz is incident on this metal, the maximum kinetic energy of the emitted electron is
(a) \( 4\times10^{-20}\ \text{J} \)
(b) \( 8\times10^{-20}\ \text{J} \)
(c) \( 2\times10^{-20}\ \text{J} \)
(d) \( 10^{-20}\ \text{J} \)
Show Answer & Explanation

Answer: (c) \( 2\times10^{-20}\ \text{J} \)

Explanation:
1. \( K=h(\nu-\nu_0)=6.63\times10^{-34}\times3\times10^{13}=2\times10^{-20} \) J.

Teacher's Note:
1. K = h (nu - nu0).

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