When a given photosensitive material is irradiated with light of frequency `nu`, 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 photosensitive material, in terms of the parameter `l`, `n` and the mass `m` of the electrons.

Explanation

(i) Einstein 's photoelectric equation
`E=hv=phi_(0)+K_(max)=phi_(0)+(1)/(2)mv_(max)^(2)` . . . (i)
where E= energy of incident photon `phi_(0)`= work function
h= planck , s constant
v = frequency of incident photon
`K_(max)=` maximum kinetic energy of photoelectron
v = maximum speed of photoelectron
m = mass of photoelectron
(ii) From equation (i),
`(1)/(2)mv_(max)^(2)=hv-phi_(0)`
`v_(max)^(2)=(2hv)/(m)-(2phi_(0))/(m)`
Comparing the above equation by y = mx +c
`m="Slope"=tantheta=(l)/(h)=(2h)/(m)rArrh=(ml)/(2h)`
Intercept on y axis `=-l=(2phi_(0))/(m)rArrphi_(0)=(ml)/(2)`