Answer
$2.5\times 10^{4}m/s$
Work Step by Step
Proton velocity, $v_{p}=5 \times 10^{4} m/s$
For proton:
By the conservation of energy;
Loss in energy = Gain in energy
$q\Delta V=\frac{1}{2}m_{p}v_{p}^{2}$ ...(1)
Now, same potential difference applied for $He^{+}$.
Thus,
Loss in energy = Gain in energy
$q\Delta V=\frac{1}{2}m_{He^{+}}v_{He^{+}}^{2}$ ...(2)
From equations (1) and (2);
$v_{He^{+}}=\sqrt {\frac{m_{p}}{m_{He^{+}}}}v_{p}$
$v_{He^{+}}=\sqrt {\frac{m_{p}}{4m_{p}}}v_{p}$
$v_{He^{+}}=\frac{v_{p}}{2} =\frac{ 5 \times 10^{4}}{2}
= 2.5\times 10^{4}m/s$
