Question

the charge to mass ratio of Alpha particle is approximately to the charge to mass ratio of proton is

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{charge}\mathrm{on}\mathrm{proton}\mathrm{be}\mathrm{e} \\ \mathrm{So},\mathrm{charge}\mathrm{on}\mathrm{\alpha }-\mathrm{particle}=2\mathrm{e} \\ \mathrm{Mass}\mathrm{of}\mathrm{proton}=\mathrm{m} \\ \mathrm{Mass}\mathrm{of}\mathrm{\alpha }-\mathrm{particle}=4\mathrm{m} \\ \mathrm{So},\mathrm{specific}\mathrm{charge}=\frac{\mathrm{Charge}}{\mathrm{Mass}} \\ \mathrm{For}\mathrm{proton},\mathrm{specific}\mathrm{charge}=\frac{\mathrm{e}}{\mathrm{m}} \\ \mathrm{For}\mathrm{\alpha }-\mathrm{particle},\mathrm{specific}\mathrm{charge}=\frac{2\mathrm{e}}{4\mathrm{m}}=\frac{\mathrm{e}}{2\mathrm{m}} \\ \mathrm{Therefore},\mathrm{ratio}=\frac{{\displaystyle \raisebox{1ex}{$\mathrm{e}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.}}{{\displaystyle \raisebox{1ex}{$\mathrm{e}$}\!\left/ \!\raisebox{-1ex}{$2\mathrm{m}$}\right.}}=2:1 \end{gathered}$$