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.
A: Statement-1 is true, Statement-2 is true, statement-2 is the correct explanation of statement-1.
B: Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
C: Statement-1 is false, Statement-2 is true.
D: Statement-1 is true, Statement-2 is false.

Hint: Kinetic energy is directly proportional to the frequency. The stopping potential depends on the frequency of incident light and nature of emitter material. Frequency of incident light is independent of its intensity. The stopping potential is directly associated with the maximum kinetic energy of electrons emitted.
Formula used:
$e{{V}_{0}}={{K}_{\max }}=hv-\varphi $
 where, $\varphi $ is the work function.
$e$ is the charge of electron
${{V}_{0}}$ is the stopping potential
$h$ is the Planck’s constant
$v$ is the frequency of light

Complete answer:
We know that,
$e{{V}_{0}}={{K}_{\max }}=hv-\varphi $
Hence, as $v$ increases both ${{V}_{0}}$ and ${{K}_{\max }}$ increases. Frequency of X –ray is greater than ultraviolet rays. Hence both ${{V}_{0}}$ and ${{K}_{\max }}$ increases.
Hence, statement I is correct.
When light energy falls on a metal surface electrons are emitted from it. The emitted electrons are called photoelectrons. This process is called the photoelectric effect. Einstein got the Nobel prize for the discovery of the photoelectric effect.
But KE ranges from zero to ${{K}_{\max }}$due to the loss of energy due to subsequent collisions before getting ejected and not due to range of frequencies within the incident light.
Hence, statement II is false.

Thus, option (D) is correct.

Additional information:
Some important conclusions arrived from photoelectric effect are,
(1) The energy distribution of the photoelectrons is independent of the intensity of incident light.
(2) The maximum kinetic energy of the photoelectrons from a given metal is found to be proportional to the frequency of the incident radiation.
(3) Photoelectrons are not emitted if the frequency of light is below the threshold value.
( 4) There seems to be no time lag between the onset of radiation and the resulting photoelectric current.

Note:
Kinetic energy is directly proportional to the frequency. The stopping potential depends on the frequency of incident light and nature of emitter material. When the ultraviolet light is replaced by X-rays, both ${{V}_{0}}$ and ${{K}_{\max }}$ increase. But kinetic energy ranges from zero to ${{K}_{\max }}$ because of the loss of energy due to subsequent collisions before getting ejected and not due to range of frequencies in the incident light.