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

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