The velocity of electron ejected from platinum surface is $6.54\times {10}^x$m/s when radiation of 200 nm falls on it. Work function of platinum is $5\mathrm{eV}.\left(1\mathrm{eV}=1.6\times {10}^{-19}\mathrm{J}\right)$. The value of x is__

Using Einstein's photoelectric equation:

         $\begin{array}{l}{E}_i=KE+\varphi \\ KE=E_i-\varphi \\ 1/2{\mathrm{mV}}^2=hv-h{v}_0\\ hv=1/2{\mathrm{mV}}^2+h{v}_{\mathrm{o}}\end{array}$

E_i: energy of incident radiation; KE: kinetic energy of electron, and $\varphi$: work function of metal

         $\begin{array}{c}{E}_i=h\frac{c}{\lambda }\\ =\frac{\left(6.63\times {10}^{-34}\right)\times \left(3\times {10}^8\right)}{200\times {10}^{-9}}=9.945\times {10}^{-19}\mathrm{J}\end{array}$

$\begin{array}{l}\varphi =5\mathrm{eV}=5\times \left(1.6\times {10}^{-19}\right)\mathrm{J}=8.0\times {10}^{-19}\mathrm{J}\\ \Rightarrow E_k=E_i-\varphi =9.945\times {10}^{-19}-8.0\times {10}^{-19}\\ \text{ Now }{E}_k=1/2m{v}^2\Rightarrow v=\sqrt{\frac{2E_k}{m}}\end{array}$

$\Rightarrow v=\sqrt{\frac{2\left(1.195\times {10}^{-19}\right)}{\left(9.1\times {10}^{-31}\right)}}=6.54\times {10}^5\mathrm{m}/\mathrm{s}$