When a given photosenstive material is irradiated with light of frequency v, and maximum speed of the emitted photoelectrons equals `v_(max)`. The square of `v_(max)`is observed to very with v, as per the graph shown in fig. Obtain expression for (i) Planck's constant and (ii) the work function of the given photosenstive material, in terms of the parameter l, n and the mass m of the electrons.

Explanation

According to Einstein's photoelectric equation
`K_(max)=1/2mv_(max)^2=hv-phi_0`
or `v_(max)^2=((2h)/m)v-(2phi_0)/m`
Thus the graph between `v_(max)^2` and v will be a straight line. Slope of st. line =`(2h)/m=l/n` intercept on `v_(max)^2` axis, `(2phi_0)/m=l` [in magnitude]
(i) `:.` Plank's constant, `h=(ml)/(2n)`
(ii) work function, `phi_0=(ml)/2`