Question

The ratio of the (e/m) ratio of an electron and an alpha particle is:

• A. 2:1
• B. 1:1
• C. 1:2
• D. None of these

Answer 1

The correct option is D None of these

Specific charge or charge/mass ratio (e/m) for an electron
Charge on electron = e = $1.6\times {10}^{-19}$ $C$
mass of electron = $m=9.1\times {10}^{-31}$ $kg$
$e/m$ of an electron = $\frac{1.6\times {10}^{-19}}{9.1\times {10}^{-31}}$ = $1.75\times {10}^{11}$ $C/kg$
For alpha particle
Charge = $2e^{-}$ = $2\times 1.6\times {10}^{-19}$ $C$
$\text{mass}=4\times \text{mass of proton}=4\times 1.67\times {10}^{-27}kg$
So $(e/m{)}_{alphaparticle}=\frac{2\times 1.6\times {10}^{-19}}{4\times 1.67\times {10}^{-27}}$
So, $\frac{(e/m{)}_{electron}}{(e/m{)}_{alphaparticle}}=\frac{(1.6\times {10}^{-19})/(9.1\times {10}^{-31})}{(2\times 1.6\times {10}^{-19})/(4\times 1.67\times {10}^{-27})}$ = 3670
So ratio of charge/mass of electron and alpha particle = 3670