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Question
Light of frequency 7.21 × 1014 Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 × 105 m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?
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Solution
Frequency of the incident photon, v = 7.21 × 1014 Hz
Maximum speed of the electrons, ν = 6.0 × 105 m/s
Planck’s constant, h = 6.626 × 10−34 Js
Mass of an electron, m = 9.1 × 10−31 kg
For threshold frequency v0, the relation for kinetic energy is written as:
`1/2 mν^2 = h(v - v_0)`
`v_0 = v - (mν^2)/(2h)`
= `7.21 xx 10^14 - ((9.1 xx 10^(-31) ) xx (6 xx 10^(5))^2)/(2 xx (6.626 xx 10^(-34)))`
= 7.21 × 1014 − 2.472 × 1014
= 4.738 × 1014 Hz
Therefore, the threshold frequency for the photoemission of electrons is 4.738 × 1014 Hz.
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