Question

Two singly ionised isotopes, X and Y of the same element move at the same speed perpendicular to a uniform magnetic field. Isotope X follows a path of radius 3.43 cm while isotope Y moves along a path 3.35 cm in radius. What is the ratio of the two isotope masses, \( m_Y / m_X \)?

• A. 0.977
• B. 0.954
• C. 1.05
• D. 1.02

Hint:

When isotopes of the same element move through a magnetic field, their masses can be compared by the ratio of their radii of curvature, given the same velocity and charge.

Answer 1

The Correct Option is D

The radius of the path in a magnetic field is given by: \[ r = \frac{mv}{qB} \] where \( m \) is the mass, \( v \) is the velocity, \( q \) is the charge, and \( B \) is the magnetic field strength. Since both isotopes move with the same velocity and charge, the ratio of their masses can be derived from the ratio of their radii: \[ \frac{r_X}{r_Y} = \frac{m_X}{m_Y} \] Substituting the given values: \[ \frac{3.43}{3.35} = \frac{m_X}{m_Y} \] which simplifies to: \[ \frac{m_Y}{m_X} = 1.02 \]