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
V2max = (l/n)ν + c
Now if V2max = 0 from graph we see ν = n
0 = (l/n)n + c
=> c = -l
V2max = (l/n)ν - l
Multiplying both sides by ½m
½ mV2max = ½m(l/n)ν -½ml
=> ½ mV2max = ½m(l/n)ν+ {-½m(l/n)}n
=> ½m(l/n)ν = ½ mV2max + {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