question_answer

When a given photosensitive material is irradiated with light of frequency \[\mathbf{v}\], the maximum speed of the emitted photoelectrons equals \[{{\upsilon }_{\max }}\] . The square of \[{{\upsilon }_{\max }},\] i.e., \[\upsilon _{\max }^{2}\]  , is observed to vary with \[\mathbf{v}\], as per the graph shown in Fig. Obtain expressions for (i) Planck's constant, and (ii) the work function of the given photosensitive material, in terms of the parameters \[l,n\] and the mass, \[\mathbf{m}\], of the electron.

Answer:

                According to Einstein?s photoelectric equation,                                 \[{{K}_{\max }}=\frac{1}{2}m\upsilon _{\max }^{2}=hv-{{W}_{0}}\]                 \[\therefore \]  \[\upsilon _{\max }^{2}=\left( \frac{2h}{m} \right)v-\frac{2{{W}_{0}}}{m}\] Thus the graph of \[\upsilon _{\max }^{2}\upsilon s.v\]is a straight equation, line.                 Clearly,                 Slope of graph,                 \[\frac{2h}{m}=\frac{l}{n}\]                 Intercept on \[\upsilon _{\max }^{2}\]axis,          \[\frac{2{{W}_{0}}}{m}=l\]                 \[\therefore \]Planck?s constant,             \[h=\frac{lm}{2n}.\]                 Work function, \[{{W}_{0}}=\frac{ml}{2}\]