Question 109: Dual Nature of Matter and Radiation

Question

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

Accepted Answer

We know,
Momentum $(p) = \sqrt {2m{E_k}} $
and ${E_k} = q{V_{acc}}$
$	herefore$ $p = \sqrt {2mq\,{V_{acc}}} $
Both $\alpha$ particle and proton are passed through same potential difference.
$	herefore$ ${\left( {{V_{acc}}} ight)_\alpha } = {\left( {{V_{acc}}} ight)_p} = v$
$	herefore$ ${p_\alpha } = \sqrt {2{m_\alpha }{q_\alpha }v} $
${p_p} = \sqrt {2{m_p}{q_p}v} $
$	herefore$ ${{{p_\alpha }} \over {{p_p}}} = \sqrt {{{{m_\alpha }{q_\alpha }} \over {{m_p}{q_p}}}} $
$ = \sqrt {{{4{m_p} 	imes 2e} \over {{m_p} 	imes e}}} $
$ = \sqrt {{8 \over 1}} $
$ = {{2\sqrt 2 } \over 1}$

Answer

$\sqrt2$ : 1

Answer

2$\sqrt2$ : 1

Answer

4$\sqrt2$ : 1

Answer

8 : 1

Dual Nature of Matter and Radiation

An \alpha particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

Choose the correct answer: