Question 155: Dual Nature of Matter and Radiation

Question

An $\alpha$ particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are $\lambda$
$\alpha$
and $\lambda$
p
respectively. The ratio ${{{{\lambda _p}} \over {{\lambda _\alpha }}}}$ is :

Accepted Answer

We know,
$qv = {{{p^2}} \over {2m}}$
$ \Rightarrow p = \sqrt {2mqv} $
$ 	herefore $ $\lambda  = {h \over {\sqrt {2mqv} }}$
$ 	herefore $ ${{{\lambda _p}} \over {{\lambda _\alpha }}} = {{\sqrt {2{m_\alpha }{q_\alpha }v} } \over {\sqrt {2{m_p}{q_p}v} }}$
$ = {{\sqrt {2(4m)(2e)} } \over {\sqrt {2me} }}$
$ = \sqrt 8 $
$ = 2\sqrt 2 $

Answer

8

Answer

2.8

Answer

7.8

Answer

3.8

Dual Nature of Matter and Radiation

An \alpha particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are \lambda \alpha and \lambda p respectively. The ratio {{{{\lambda _p}} \over {{\lambda _\alpha }}}} is :

Choose the correct answer: