Question

A student was performing an experiment to demonstrate the photoelectric effect. When the student shined light from the source on the metal surface, no electrons were ejected. Which of the following could explain the observed result? Select one: a. The light intensity was insufficient. b. The energy of the light was too high. c. The frequency of the light was too low. d. The wavelength of the light was too short.

Answer 1

Ans. For ejection of electrons, the specified metal surface must be irradiated with a light equal to or higher than its threshold frequency. The threshold frequency indirectly measures the minimum energy required to eject the electron from metal’s orbital.

Energy of the photon is given by-

            E = hv            - equation 1

; where, h = Plank’s constant = 6.626 x 10^-34 Js   ; v = frequency of photon   

In equation 1, note that the energy of a photon (quantum of light) is proportional to its frequency.

Option A. Incorrect. Intensity is the relative abundance of photons falling per unit area of the specified surface. Suppose a metal requires photons with threshold frequency in range of violate rays to eject electrons. If the metal surface is irradiated with very few photons of violet rays, electrons would be ejected because the photons have sufficient energy. However, if the metal surface is irradiated with extremely intense with red light, no electrons would be ejected because the photons of red light have much lower energy than required for photoelectric effect.

Since, the quality of light is not specified, it is not the most appropriate option.

Option B. Incorrect. If the energy were too high, electrons would have been ejected. See paragraph 1.

Option C. Correct. Since the frequency is too low, lesser than the threshold frequency, no photoelectric effect would be observed., Note that lower is the frequency, lower would be the energy of the photon (see equation 1). It is the most appropriate option. Irradiating the metal surface with photons of frequency equal to or higher than threshold frequency ejects electrons irrespective of its intensity.

Option D. Incorrect. Wavelength of an electromagnetic radiation is inversely proportional to its frequency. It is given by the equation-

                        c = v l                      - equation 2

            Where, c = speed of light = 299792458 m/s

                        v = frequency

                        l = wavelength

Given, ‘wavelength too short’. Smaller is the wavelength, higher is the frequency. So, too short wavelength = very high frequency would be capable of ejecting electrons from metal surface.