Question

The specific charge of proton is $9.6\times {10}^{7}C{kg}^{-1}$, then for an $\alpha$-particle it will be :

• A. $38.4\times {10}^{7}C{kg}^{-1}$
• B. $19.2\times {10}^{7}C{kg}^{-1}$
• C. $2.4\times {10}^{7}C{kg}^{-1}$
• D. $4.8\times {10}^{7}C{kg}^{-1}$

Answer 1

The correct option is D $4.8\times {10}^{7}C{kg}^{-1}$

As given that proton has specific charge to be $9.6\times {10}^{7}Ck{g}^{-1}.$

Now as alpha particle is the Helium nucleus, so it must have +2 unit charge.
Specific charge of proton $=\frac{specificchargeofproton}{massofprotoninparticle}$

Alpha particle is doubly ionised He atom. It carries +2e charge (Twice the charge of proton and mass of alpha particle is (2 Neutrons + 2 Protons) is almost 4 times the mass of proton.

So, if Specific charge of Proton = $\frac{+e}{m_p}$

Then, Specific charge of Alpha particle = $\frac{+2e}{4m_p}=$ specific charge of proton $\times$ 1/2

So, Specific charge of alpha particle $=\frac{9.6\times {10}^7}{2}=4.8\times {10}^{7}Ck{g}^{-1}.$