A deuteron and an \( \alpha \)-particle moving with the same velocity enter into a uniform magnetic field acting normal to the plane of their motion. The ratio of the circular paths described by the deuteron and \( \alpha \)-particle is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 : 1
A charged particle moving perpendicular to a uniform magnetic field goes round a circle because the magnetic force supplies the centripetal force: \( qvB = \frac{mv^{2}}{r} \), so \( r = \frac{mv}{qB} \). For the same speed and the same field, \( r\propto\frac{m}{q} \).
A deuteron has one proton and one neutron, so \( m_d \approx 2m_p \) and \( q_d = e \). An α particle has two protons and two neutrons, so \( m_\alpha \approx 4m_p \) and \( q_\alpha = 2e \).
\( \displaystyle \frac{r_d}{r_\alpha} = \frac{m_d}{m_\alpha}\times\frac{q_\alpha}{q_d} = \frac{2m_p}{4m_p}\times\frac{2e}{e} = 1 \)
The ratio is 1 : 1.