If the frequency of radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be K.
Option D is correct
The maximum kinetic energy (K) of photoelectrons ejected from a metal when illuminated with light depends on the relationship:
K = hv - E₀
hv = the photon energy (h is Planck's constant and v is the frequency)
E₀ = the work function of the metal (energy required to eject an electron)
When the frequency of the radiation is doubled (2v), the photon energy also doubles (2hv):
K = (2hv) - E₀
K = 2hv - E₀
We now compare this with the original equation:
K = hv - E₀ and see that the maximum kinetic energy remains the same (K) when the frequency is doubled.
In conclusion, the doubling of the frequency only provides enough energy for the photons to overcome the work function and eject more electrons, but it do not increase the energy of the initially ejected electrons with the highest kinetic energy (K).