Ratio of momenta of an electron and an α - particle which are accelerated from rest by a potential

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11.Dual Nature of Radiation and matter

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The ratio of momenta of an electron and an $\alpha - $particle which are accelerated from rest by a potential difference of $100 V$ is

A

$1$

B

$\sqrt {\frac{{2{m_e}}}{{{m_\alpha }}}} $

C

$\sqrt {\frac{{{m_e}}}{{{m_\alpha }}}} $

D

$\sqrt {\frac{{{m_e}}}{{2{m_\alpha }}}} $

Solution

(d) Momentum $p = mv$ and $v = \sqrt {\frac{{2QV}}{m}} $

==> $p = \sqrt {2QmV} $

==> $p \propto \sqrt {Qm} $

==>$\frac{{{p_e}}}{{{p_\alpha }}} = \sqrt {\frac{{e \times {m_e}}}{{2e \times {m_\alpha }}}} = \sqrt {\frac{{{m_e}}}{{2{m_\alpha }}}} $

Standard 12

Physics

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