Question

What was the initial speed of the alpha particle?

• A. $132.\times {10}^{2}m{s}^{-1}$
• B. $\mathrm{1.32.}\times {10}^{7}m{s}^{-1}$
• C. $\mathrm{13.2.}\times {10}^{2}m{s}^{-1}$
• D. $\mathrm{0.13.}\times {10}^{7}m{s}^{-1}$

Answer 1

The correct option is B $\mathrm{1.32.}\times {10}^{7}m{s}^{-1}$

As alpha particle goes near nucleus its K.E gets converted to Potential energy and its velocity becomes zero.
$\Rightarrow \frac{k{q}_1{q}_2}{r}=\frac{1}{2}m{v_i}^2+0$

$\Rightarrow v_i=\sqrt{\frac{2k{q}_1{q}_2}{rm}}$

Therefore, initial velocity is:
$\Rightarrow v_i=\sqrt{\frac{2(8.97\times {10}^9)\times 82\times 2\times {(1.602\times {10}^{-19})}^2}{(6.5\times {10}^{-14})\times (6.64\times {10}^{-27})}}=1.322\times {10}^{7}m/s$