Question 176: 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 $\alpha particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are \lambda\alpha and \lambdap respectively. The ratio {{{{\lambda _p}} \over {{\lambda _\alpha }}}}$ is :

Choose the correct answer: