Read the following passage and answer the questions.
A student studies a photocell. It is an evacuated glass tube with a quartz window. Inside the tube are an emitter plate C and a collector plate A. Plate C is coated with a metal that gives out electrons even in red light. A battery and a commutator let her make plate A positive or negative with respect to C. A microammeter reads the photocurrent.
In the first run, she shines a red laser pointer on plate C. The light has a wavelength of 620 nm, and the pointer gives out a power of 2.4 mW. She records the photocurrent as she changes the potential of A from positive to negative values. In the second run, she uses a red laser of the same wavelength but twice the power. In the third run, she uses a violet laser of wavelength 410 nm. She adjusts it so that the same number of photons reach plate C each second as in the first run.
(Take \(hc = 1240\ \mathrm{eV\,nm}\) and \(1\ \mathrm{eV} = 1.6\times10^{-19}\ \mathrm{J}\).)
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In the second run, the maximum kinetic energy of the photoelectrons is twice its value in the first run.
Reason (R): All photons of light of a given wavelength have the same energy, whatever the intensity of the light.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) is not correct but (R) is correct.
Assertion (A) In the second run, the maximum kinetic energy of the photoelectrons is twice its value in the first run. — False. Twice the power means twice as many photons reach plate C each second. Each photon still has the energy of 620 nm light. By Einstein’s equation \( K_{\max}=h\nu-\phi_0 \), the maximum kinetic energy stays the same. Only the number of photoelectrons emitted each second doubles.
Reason (R) All photons of light of a given wavelength have the same energy, whatever the intensity of the light. — True. The energy of a photon is \( E=hc/\lambda \), which depends only on the wavelength. A brighter beam only has more photons per second.
NCERT (2026-27):
Effect of frequency of incident radiation on stopping potential – “The maximum kinetic energy of the photoelectrons varies linearly with the frequency of incident radiation, but is independent of its intensity.”
Particle Nature of Light: the Photon – “(iii) All photons of light of a particular frequency ν, or wavelength λ, have the same energy E (=hν = hc/λ) and momentum p (= hν/c= h/λ), whatever the intensity of radiation may be. …”