Ultraviolet light of wavelengths $800\stackrel{\circ }{A}$ and $700\stackrel{\circ }{A}$when allowed to fall on hydrogen atoms in their ground and  is found to liberate electrons with kinetic energy 1.8 ev and $4.0eV$ respectively. Find the value of Planck's constant.

 

When $800\stackrel{\circ }{A}$wavelength falls on hydrogen atom (in ground state) $13.6cV$  energy is used in liberating the electron. The rest is given as kinetic energy to the electron.

Hence,  $(K=E-13.6) (in eV)$

$\Rightarrow \left(1.8\times 1.6\times {10}^{-19}\right)=\frac{hc}{800\times {10}^{-10}}-13.6\times 1.6\times {10}^{-19}$………..(i)

Similarly, for the second wavelength, we have

$\left(4\times 1.6\times {10}^{-19}\right)=\frac{hc}{700\times {10}^{-10}}-13.6\times 1.6\times {10}^{-19}\dots ......\left(2\right)$

Solving these two equations, we get

$h=6.6\times {10}^{-34}Js$