(i) Kinetic energy of alpha particle K.E. = qv
\(\frac12mv^2= 2e \times100\)
\(\frac12mv^2= 200 \,ev\)
\(v^2 = \frac{400\,ev}{m}\)
\(v= \sqrt{\frac{400\,ev}{m}}\)
\(v = \sqrt{\frac{400\times1.6\times10^{19}}{6.4\times10^{27}}}\)
\(v =\sqrt{\frac{640}{64}\times10^8}\)
\(v = \sqrt{100\times10^8}\)
v = 10 x 104 m/s
(ii) Kinetic energy gained by alpha particle by potential difference 100 V is
\(\frac{p^2}{2m_\alpha}= q_\alpha v\)
\(\frac{p^2}{2m_\alpha}= 2\,ev\)
\(p^2 = 4m_\alpha ev\)
\(p = \sqrt{4m_\alpha ev}\)
\(p= \sqrt{4\times6.4\times10^{-27}\times1.6\times10^{-19}\times100}\)
\(p = \sqrt{4096\times10^{-46}}\)
\(p = 64 \times 10^{-23}\)
de-Broglie wavelength,
\(\lambda=\frac hp\)
\(\lambda=\frac{6.64\times10^{-34}}{64\times10^{-23}}\)
\(\lambda = 0.103 \times 10^{-11}\)
\(\lambda = 0.0103 \times 10^{-10}\)
\(\lambda = 0.0103 \,A^o\)