JEE MAIN - Physics (2010 - No. 5)
Statement - $$1$$ : When ultraviolet light is incident on a photocell, its stopping potential is $${V_0}$$ and the maximum kinetic energy of the photoelectrons is $${K_{\max }}$$. When the ultraviolet light is replaced by $$X$$-rays, both $${V_0}$$ and $${K_{\max }}$$ increase.
Statement - $$2$$ : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.
Statement - $$1$$ is true, Statement - $$2$$ is true; Statement - $$2$$ is the correct explanation of Statement - $$1$$
Statement - $$1$$ is true, Statement - $$2$$ is true; Statement - $$2$$ is not the correct explanation of Statement - $$1$$
Statement - $$1$$ is is false, Statement - $$2$$ is true
Statement - $$1$$ is is true, Statement - $$2$$ is false
Explanation
Statement 1 is true. The energy of an incident photon (from the ultraviolet light or X-rays) on a photocell is given by Planck's equation, $E = h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency of the light. X-rays have a higher frequency than ultraviolet light, so they deliver more energy to the photoelectrons. This results in a higher stopping potential ($V_0$) and maximum kinetic energy ($K_{\max}$) for the photoelectrons.
Statement 2 is also true. However, while the speeds (and hence kinetic energies) of photoelectrons do vary, this variation is not because of a range of frequencies in the incident light. Rather, it's due to the interaction of the incident photons with electrons at different energy levels in the metal. A single frequency of light can produce photoelectrons with a range of speeds because the electrons they encounter can have a variety of binding energies.
Statement 2 is also true. However, while the speeds (and hence kinetic energies) of photoelectrons do vary, this variation is not because of a range of frequencies in the incident light. Rather, it's due to the interaction of the incident photons with electrons at different energy levels in the metal. A single frequency of light can produce photoelectrons with a range of speeds because the electrons they encounter can have a variety of binding energies.
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