Helium at a low pressure is contained within a discharge tube. A...

Let $E$ be the electric field applied across the discharge tube.

The force on the free electron is $F_e = eE$, and its acceleration is $a_e = \dfrac{eE}{m_e}$.

Since the helium atom is ionized by the detachment of a single electron, the charge on the helium ion (He^+$) is$+e$.<br><br>The force on the helium ion is$F_i = eE$, and its acceleration is$a_i = \dfrac{eE}{m_i}$.<br><br>The distance travelled by a particle starting from rest in a short time interval$dt$is given by$s = \dfrac{1}{2}a(dt)^2$.<br><br>The ratio of the distances travelled by the electron and the helium ion is:<br><br>$\dfrac{s_e}{s_i} = \dfrac{a_e}{a_i} = \dfrac{m_i}{m_e}$<br><br>The mass of a helium ion is approximately$4$times the mass of a proton ($m_p$).<br><br>$m_i \approx 4m_p$<br><br>Using the standard ratio$\dfrac{m_p}{m_e} \approx 1836$, we get:<br><br>$\dfrac{s_e}{s_i} \approx 4 \times 1836 = 7344$<br><br>The closest value among the given options is$7340.