Light of frequency 7.21 x 10¹⁴ Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 x 10⁵ m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?

Solution

Given,
Frequency of light, $ν$ = 7.21 x 10¹⁴ Hz
Maximum speed of electrons, v_max = 6.0 x 10⁵ ms^–1Mass of the electron, m = 9 x 10^–31 kg

Applying Einstein's photoelectric equation,
   $K . E ._{\max} = \frac{1}{2} {mv}^{2}_{\max} = h (v - v_{0})$

$\Rightarrow$ $\frac{1}{2} {mv}^{2}_{\max} = h (v - v_{0})$
$\Rightarrow$    $v_{0} = v - \frac{{mv}^{2}_{\max}}{2 h}$
$\Rightarrow$    $v_{0} = 7.21 \times 10^{14} - \frac{(9.1 \times 10^{- 31}) \times (6 \times 10^{5})^{2}}{2 \times (6.63 \times 10^{- 34})}$
$= 4.74 \times 10^{14} Hz .$

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Light of frequency 7.21 x 10¹⁴ Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 x 10⁵ m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?

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Light of frequency 7.21 x 10¹⁴ Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 x 10⁵ m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?