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Atomic Structure

Section: Chemistry

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Question : 14 of 32

Marks: +1, -0

When a metal surface is irradiated with light of frequency

x\,\mathrm{Hz}

, the kinetic energy of emitted photoelectrons is

z\,\mathrm{J}

. When the same metal is irradiated with light of frequency

y\,\mathrm{Hz}

, the kinetic energy of emitted electrons is

\;\frac{z}{3}\,\mathrm{J}

. What is the threshold frequency (in Hz) of metal?

[AP EAPCET 21 May 2025 S1]

$\;\frac{3}{2}(y-x)$
$\left(\;\frac{3 y - x}{2}\right)$
$\left(\;\frac{2 y - x}{3}\right)$
$\;\frac{2}{3}(y-x)$

Solution:

Kinetic energy, when

x

frequency light is irradiated

z = h (x-f_0)

Kinetic energy, when

y

frequency light is irradiated

\;\frac{z}{3} = h [y-f_0]

divide Eq. (i) and (ii)

\;\frac{z}{\frac{z}{3}} = \;\frac{h (x-f_0)}{h (y-f_0)} \Rightarrow 3 = \;\frac{x-f_0}{y-f_0}

On solving for

f_0

f_0 = \;\frac{3 y - x}{2}

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