Question

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

• A. 1
• B. $\sqrt{\frac{2m_e}{m_{\alpha }}}$
• C. $\sqrt{\frac{m_e}{m_{\alpha }}}$
• D. $\sqrt{\frac{m_e}{2m_{\alpha }}}$

Answer 1

The correct option is D $\sqrt{\frac{m_e}{2m_{\alpha }}}$

$\frac{Pe}{Pa}=\sqrt{(}\frac{MeQe}{MaQa})$

where,

$Me=massofelectron$

$Ma=massofalphaparticle$

$Qe=chargeofelectron$

$Qa=chargeofalphaparticle$

we know,

$Qa=2Qe$

therefore

$\frac{Pe}{Pa}=\sqrt{(}\frac{MeQe}{2MaQe})$

So we get,

$\frac{Pe}{Pa}=\sqrt{(}\frac{Me}{2Ma})$.