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: