Question

The charge to mass ratio of an alpha particle is:

• A. 2 times the $\frac{e}{m}$ value of an electron
• B. 4 times the $\frac{e}{m}$ value of an electron
• C. 2 times the $\frac{e}{m}$ value of a proton
• D. $\frac{1}{2}$times the $\frac{e}{m}$ value of a proton

Answer 1

The correct option is D $\frac{1}{2}$times the $\frac{e}{m}$ value of a proton

Alpha particles are basically helium nuclei.
${}_2^{4}He\to H{e}^{2+}+2e^{-}$

$H{e}^{2+}$ is an alpha particle which has two protons and two neutrons and a $+2$ relative unit charge.
The mass of a proton $\left(m_p\right)$ is approximately equal to the mass of a neutron $\left(m_n\right)$ i.e. $m_p=m_n$
So, the total mass of an alpha particle is approximately 4 times than that of a proton and the charge on an alpha particle is twice than that of the charge on a proton.
$\frac{(e/m{)}_{\text{alpha}}}{(e/m{)}_{\text{proton}}}=\frac{(2e/4m{)}_{\text{proton}}}{(e/m{)}_{\text{proton}}}=\frac{e_p}{2m_p}=\frac{1}{2}\left(\frac{e}{m}\text{of proton}\right)$