Which one of the following statements on photoelectric effect is NOT correct?

Correct — C, At a frequency ν > ν₀, the kinetic energy of ejected electrons does not change on increasing the frequency of incident light. This is the one false statement. Einstein's photoelectric equation gives the maximum kinetic energy as hν minus the work function, so it climbs in a straight line as the frequency of the light is raised. A graph of maximum kinetic energy against frequency is a straight line whose slope is the Planck constant, which is how h was first measured this way.

• (a)Albert Einstein received the Nobel Prize in Physics for explaining photoelectric effect — True. Einstein received the Nobel Prize in Physics for 1921 for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect, not for relativity.
• (b)For each metal, there is a threshold frequency ν₀ below which this effect is not observed — True, and central. Below the threshold frequency no electron is ejected however intense the light, because a single photon simply lacks the energy needed to free one.
• (d)The number of electrons ejected is proportional to the intensity of incident light — True. Intensity fixes the number of photons arriving each second, so it fixes the number of electrons ejected — but not the energy each one carries away.

Light of frequency ν delivers its energy in indivisible quanta of size hν. One photon frees at most one electron, and it must supply the work function φ, the minimum energy holding an electron inside the metal. Whatever is left over appears as kinetic energy, giving KEmax = hν − φ. Frequency therefore controls the energy of each ejected electron, and intensity controls how many are ejected.

The two knobs are the whole of the phenomenon, and every wrong statement examiners write about it confuses them. Classical wave theory predicted that bright enough light of any colour would eventually free electrons, and that the effect would take time to build up. Experiment shows neither: dim ultraviolet works instantly while intense red light does nothing at all. That failure is what forced the photon on physics, and this item's option (b) is the threshold on which the whole argument rests.

• Einstein's photoelectric equation is KEmax = hν − φ, with φ the work function of the metal.
• The threshold frequency ν₀ satisfies hν₀ = φ; below it no electron is emitted regardless of intensity.
• The maximum kinetic energy rises linearly with frequency and does not depend on intensity.
• The number of photoelectrons emitted per second is proportional to the intensity of the incident light.
• Einstein was awarded the 1921 Nobel Prize in Physics for the law of the photoelectric effect.

• Letting intensity change the energy of individual photoelectrons, when it only changes their number.
• Expecting a bright enough source of any colour to eventually eject electrons.
• Attributing Einstein's Nobel Prize to relativity.

A NOT-correct item across the standard four facts. Learning which quantity each knob controls answers almost every version of this question.

• practice — not a real PYQ

  In the photoelectric effect, increasing the intensity of the incident light while keeping its frequency unchanged results in

  • (a)a higher maximum kinetic energy of the photoelectrons
  • (b)a larger number of photoelectrons emitted per second
  • (c)a lower threshold frequency
  • (d)no emission at all

  Answer(b) a larger number of photoelectrons emitted per second — intensity fixes the photon count, not the energy of each photon.

• practice — not a real PYQ

  The slope of a graph of the maximum kinetic energy of photoelectrons against the frequency of incident light gives

  • (a)the work function of the metal
  • (b)the Planck constant
  • (c)the charge on an electron
  • (d)the threshold frequency

  Answer(b) the Planck constant — the equation KEmax = hν − φ is a straight line of slope h and intercept −φ.