# Question contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.Statement-1 : When ultraviolet light is incident on a photocell, its stopping potential is $\dpi{100} V_{0}$ and the maximum kinetic energy of the photoelectrons is $\dpi{100} K_{max}$. When the ultraviolet light is replaced by X-rays, both $\dpi{100} V_{0}$ and $\dpi{100} K_{max}$ 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. Option 1) Statement-1 is true, Statement-2 is false. Option 2) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1. Option 3) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1. Option 4) Statement-1 is false, Statement-2 is true.

As we learnt in

Conservation of energy -

$h\nu = \phi _{0}+\frac{1}{2}mv^{2}_{max}$

$h\nu = h\nu _{0}+\frac{1}{2}mv^{2}_{max}$

$h\left ( \nu-\nu _{0} \right )=\frac{1}{2}mv^{2}_{max}$

$where, h - Plank's constant\ \nu - Frequency\ \nu_{0} - threshold\ frequency\ \phi_{0}- work function$

- wherein

From Einstein's photoelectric equation

$eV_{0}=h{\nu}-{\phi}$                                (1)

Also  $eV_{0}=K_{max}$                            (2)

When we increase energy of photon (i.e. moving from ultraviolet to X-ray)

V0 increases andhence Kmax also increases.

So Statement (1) is correct.

Statement (2) is wrong as speed of electron varies because of its collision inside the metal before its emission.

Option 1)

Statement-1 is true, Statement-2 is false.

This is the correct option.

Option 2)

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

This is an incorrect option.

Option 3)

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

This is an incorrect option.

Option 4)

Statement-1 is false, Statement-2 is true.

This is an incorrect option.

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