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Question
The work function of a metal is 2.5 × 10−19 J. (a) Find the threshold frequency for photoelectric emission. (b) If the metal is exposed to a light beam of frequency 6.0 × 1014 Hz, what will be the stopping potential?
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
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Solution
Given :-
Work function of a metal, W0 = 2.5 × 10−19 J
Frequency of light beam, v = 6.0 × 1014 Hz
(a) Work function of a metal,
W0 = hv0,
where h = Planck's constant
v0 = threshold frequency
`therefore "v"_0 = W_0/h`
`⇒ v_0 = (2.5 xx 10^-19)/(6.63 xx 10^-34)`
`= 3.77 xx 10^14 "Hz"`
`= 3.8 xx 10^14 "Hz"`
(b) Einstein's photoelectric equation :-
`eV_0 = hv - W_0`,
where
v = frequency of light
V0 = Stopping potential
e = charge on electron
`therefore V_0 = (hv - W_0)/e`
`= (6.63 xx 10^-34 xx 6 xx 10^14 - 2.5 xx 10^-19)/(1.6 xx 10^-19)`
`= (3.97 xx 10^-19 - 2.5 xx 10^-19)/(1.6 xx 10^-19) = 0.91 V`
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