\(R=\frac{m v}{B q}\) or \(m v=R B q\)
Here, \(R=0.83\,\mathrm{cm}=0.83 \times 10^{-2}\, \mathrm{m}\)
\(B=0.25\,\mathrm{Wb}\mathrm{m}^{-2}\)
\(q=2e=2 \times 1.6 \times 10^{-19} \mathrm{C}\)
\(\therefore mv = \) \(\left( {0.83 \times {{10}^{ - 2}}} \right)(0.25)\left( {2 \times 1.6 \times {{10}^{ - 19}}} \right)\)
de Broglie wavelength,
\(\lambda = \frac{h}{{mv}} = \) \(\frac{{6.6 \times {{10}^{ - 34}}}}{{0.83 \times {{10}^{ - 2}} \times 0.25 \times 2 \times 1.6 \times {{10}^{ - 19}}}}\)
\( = 0.01\,\mathop A\limits^o \)
( ફોટોનની ઊર્જા $ = \frac{{1240}}{{\lambda {\rm{(in\, nm)}}}}\,eV$)
(પ્લાંક અચળાંક $\left. h =6.62 \times 10^{-34}\, J . s \right)$