question_answer

What is the ratio of specific charge of proton to that of an alpha particle? (Hint: mass of \[\alpha \]- particle\[=\text{4}\times \text{1}.\text{66}\times \text{1}{{0}^{-\text{24}}}\text{g}\])

Answer:

Specific charge of a proton (\[{{S}_{1}}\]) \[=9.58\times {{10}^{4}}C/g\] Let us now find the specific charge (\[{{S}_{2}}\]) of\[\alpha \]particle. Charge on \[\alpha \] - particle \[(H{{e}^{+2}})=2\times 1.6\times {{10}^{-19}}C\] Mass of \[\alpha \]- particle\[=4\times 1.66\times {{10}^{24}}g\] \[\therefore \]\[{{S}_{2}}=\frac{2\times 1.6\times {{10}^{-19}}}{4\times 1.6\times {{10}^{-24}}}=5\times {{10}^{4}}C/g\] \[\therefore \]\[\frac{{{S}_{1}}}{{{S}_{2}}}=\frac{9.58\times {{10}^{4}}}{5\times {{10}^{4}}}=\frac{2}{1}\] Therefore, the ratio of specific charge of proton to that of an alpha particle is 2 : 1.