(a) Use Einstein photoelectric equation to depict the variation of the maximum kinetic energy (Ek) of electrons emitted, with the frequency (v) of the incident radiation.
(b) A photosensitive surface is illuminated with a beam of (i) yellow light, and (ii) red light, both of the same intensity. In which case will
(I) photoelectrons have more Ek?
(II) more numbers of electrons be emitted? Justify your answer in each case.
 

(a)

Part (a): Variation of Maximum Kinetic Energy with Frequency

The Einstein photoelectric equation is given by:

E_k,max = hv - hv₀

Here:

• h is Planck's constant
• v is the frequency of the incident radiation
• v₀ is the threshold frequency
  • E_k,max is the maximum kinetic energy of the emitted photoelectrons

The maximum kinetic energy (E_k,max) increases linearly with the frequency (v) of the incident radiation above the threshold frequency (v₀). Below the threshold frequency, no photoelectrons are emitted, as the energy of the photons is insufficient to overcome the work function of the material. The graph between E_k,max and v will start at v₀ and increase linearly.

Part (b): Comparison for Yellow and Red Light

(i) Photoelectrons with Higher Kinetic Energy

Using the Einstein photoelectric equation, the energy of incident photons depends on their frequency (v). Yellow light has a shorter wavelength than red light, meaning yellow light has a higher frequency. According to E = hv, yellow light photons carry more energy than red light photons.

Thus, the photoelectrons emitted under yellow light will have higher maximum kinetic energy (E_k,max) compared to those emitted under red light.

(ii) Number of Electrons Emitted

The Einstein photoelectric equation states that photoemission occurs only if the frequency of the incident light exceeds the threshold frequency (v₀) of the material.

• Red light has a lower frequency than yellow light. If the frequency of red light is below the material's threshold frequency (v₀), it will not cause any photoemission.
• Yellow light, having a frequency greater than or equal to the threshold frequency (v₀), will cause photoemission, resulting in more electrons being emitted.

In summary:

• Kinetic Energy of Photoelectrons: Higher under yellow light than red light.
• Number of Photoelectrons Emitted: Yellow light will emit more electrons than red light.