When a given photosensitive material is irradiated with light of frequency V , the maximum speed of the emitted photoelectrons equals Vmax. The square of Vmax, i.e., Vmax2, is observed to vary with , as per the graph shown here. Obtain expressions

(i) Planck’s constant, and

(ii) The work function of the given

photosensitive material,

in terms of the parameters n and the mass, m, of the electron.

According to the graph

y = kx + c

From graph slope of the graph k = l/n

V^{2}_{max}^{ } = (l/n)*ν *+ c

Now if V^{2}_{max} = 0 from graph we see ν = n

0 = (l/n)*n *+ c

=> c = -l

V^{2}_{max} = (l/n)*ν *- l

Multiplying both sides by ½m

½ mV^{2}_{max} = ½m(l/n)*ν *-½ml

=> ½ mV^{2}_{max}^{ } = ½m(l/n)ν+* *{-½m(l/n)}n

=> ½m(l/n)ν = ½ mV^{2}_{max} + {½m(l/n)}n

Comparing with photoelectric equation

hν = KE + W

1. Planck’s constant h = ½m(l/n)

2. Work function = {½m(l/n)}n = ½ml

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