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Dual Nature of Radiation and Matter — NEET & JEE MCQs with answers
This chapter establishes the dual nature of electromagnetic radiation and matter, covering the photoelectric effect, Einstein's photon picture, and de Broglie's matter-wave hypothesis. It shows that the nature of an experiment decides whether a wave or a particle description of radiation suits it best, and that moving material particles likewise have an associated wavelength $\lambda = h/p$.
Topics in this chapter
- 11.1 Introduction
- 11.2 Electron Emission
- 11.3 Photoelectric Effect
- 11.4 Experimental Study of Photoelectric Effect
- 11.5 Photoelectric Effect and Wave Theory of Light
- 11.6 Einstein's Photoelectric Equation: Energy Quantum of Radiation
- 11.7 Particle Nature of Light: The Photon
- 11.8 Wave Nature of Matter
Free practice questions
A metal has work function $2.5$ eV. The longest wavelength (threshold wavelength) that can eject photoelectrons, $\lambda_0=hc/\phi_0$, is (take $hc=1.99\times10^{-25}$ J·m):
- A. $9.95\times10^{-7}$ m
- B. $2.01\times10^{6}$ m
- C. $7.96\times10^{-26}$ m
- D. $4.97\times10^{-7}$ m
Show answer
Answer: D — $\lambda_0=\dfrac{hc}{\phi_0}=\dfrac{1.99\times10^{-25}}{4\times10^{-19}}=4.97\times10^{-7}$ m.
NCERT Class 12 Physics Ch 11 ("there exists a threshold frequency")
Which scientist connected a zinc plate to an electroscope in 1888 and observed charge changes under ultraviolet light?
- A. Philipp Lenard
- B. Heinrich Hertz
- C. Wilhelm Hallwachs
- D. J. J. Thomson
Show answer
Answer: C — NCERT: Hallwachs, in 1888, connected a negatively charged zinc plate to an electroscope.
NCERT Class 12 Physics Ch 11 ("Hallwachs, in 1888, undertook the study further")
Only the frequency of light is increased (intensity fixed). Which observation is correct?
- A. Higher saturation current, same stopping potential
- B. Same saturation current, more negative stopping potential
- C. Higher saturation current, more negative stopping potential
- D. Same saturation current, less negative stopping potential
Show answer
Answer: B — Per NCERT: “The stopping potential is more negative for higher frequencies of incident radiation”. Hence the correct choice is: Same saturation current, more negative stopping potential.
NCERT Class 12 Physics Ch 11 ("The stopping potential is more negative for higher frequencies of incident radiation")
A photon has frequency $6\times10^{14}$ Hz. Using $p=h\nu/c$, its momentum is (take $h=6.63\times10^{-34}$ J·s, $c=3\times10^{8}$ m/s):
- A. $2.65\times10^{-27}$ kg·m/s
- B. $1.19\times10^{-10}$ kg·m/s
- C. $1.33\times10^{-27}$ kg·m/s
- D. $3.98\times10^{-19}$ kg·m/s
Show answer
Answer: C — $p=\dfrac{h\nu}{c}=\dfrac{6.63\times10^{-34}\times6\times10^{14}}{3\times10^{8}}=1.33\times10^{-27}$ kg·m/s.
NCERT Class 12 Physics Ch 11 ("associated with momentum")
At equal speeds, the ratio of the de Broglie wavelength of a proton (mass $1.67\times10^{-27}$ kg) to that of an alpha particle (mass $6.64\times10^{-27}$ kg) is $\lambda_1/\lambda_2=m_2/m_1$. It equals:
- A. $1$
- B. $3.98$
- C. $0.252$
- D. $1.11\times10^{-53}$
Show answer
Answer: B — $\dfrac{\lambda_1}{\lambda_2}=\dfrac{m_2}{m_1}=3.98$; the heavier particle has the shorter wavelength.
NCERT Class 12 Physics Ch 11 ("l is smaller for a heavier particle")
The work function of a metal is generally denoted by which symbol?
- A. $\lambda_0$
- B. $\phi_0$
- C. $\nu_0$
- D. $K_{max}$
Show answer
Answer: B — NCERT states that the work function is generally denoted by $\phi_0$ and measured in eV (electron volt).
NCERT Class 12 Physics Ch 11 ("It is generally denoted by f0 and measured in eV (electron volt)")
The fact that $e/m$ was independent of the cathode material and the gas used suggested what conclusion?
- A. That charge is not quantised
- B. That the particles travel at the speed of light
- C. That the particles were positively charged
- D. The universality of the cathode ray particles
Show answer
Answer: D — This observation suggested the universality of the cathode ray particles — they were the same regardless of the source.
NCERT Class 12 Physics Ch 11 ("the universality of the cathode ray particles")
Why does the wave theory predict that even low-frequency light, if intense enough and given enough time, should cause photoemission?
- A. Because electrons multiply under illumination
- B. Because a sufficiently intense beam over enough time can supply the needed escape energy
- C. Because the work function decreases with time
- D. Because low-frequency photons carry more energy
Show answer
Answer: B — In the wave picture a sufficiently intense beam over sufficient time should impart enough energy to the electrons to exceed the escape energy, regardless of frequency — hence no threshold should exist.
NCERT Class 12 Physics Ch 11 ("A threshold frequency, therefore, should not exist.")
The most energetic photoelectrons have maximum kinetic energy $K_{max}$. The stopping potential $V_0$ is related to it by:
- A. $K_{max} = \tfrac{1}{2}eV_0$
- B. $K_{max} = eV_0$
- C. $K_{max} = eV_0^2$
- D. $eK_{max} = V_0$
Show answer
Answer: B — Per NCERT: “Kmax = e V0”. Hence the correct choice is: K_{max} = eV_0.
NCERT Class 12 Physics Ch 11 ("Kmax = e V0")
Light of frequency $1.2\times10^{15}$ Hz is incident on a metal of work function $3$ eV. The stopping potential $V_0=\dfrac{h\nu}{e}-\dfrac{\phi_0}{e}$ is (use $h=6.63\times10^{-34}$ J·s, $e=1.6\times10^{-19}$ C):
- A. $1.97$ V
- B. $4.97$ V
- C. $3$ V
- D. $0.986$ V
Show answer
Answer: A — $\dfrac{h\nu}{e}=4.97$ V; $V_0=4.97-3=1.97$ V.
NCERT Class 12 Physics Ch 11 ("the electron is emitted with maximum kinetic energy")
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