# This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements :Statement - 1 : A metallic surface is irradiated by a monochromatic light of frequency  $\dpi{100} \upsilon > \upsilon _{0}$  (the threshold frequency). The maximum kinetic energy and the stopping potential are $\dpi{100} K_{max}\;$ and $\dpi{100} V_{0}$  respectively. If the frequency incident on the surface is doubled, both the   $\dpi{100} K_{max}\;$ and $\dpi{100} V_{0}$  are also doubled.Statement - 2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of 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.

Aw 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

When frequency is doubled maximum kinetic energy and stopping potential become more than double.

$K_{max}=eV_{0}=h{\nu}-h{\nu_{0}}$                                (1)

So statement 1 is false.

Graph between maximum kinetic energy or stopping potential with frequency is linear.

So statement 2 is true.

Option 1)

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

This is an incorrect 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 the correct option.

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