HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q42 Solution: A narrow beam of singly charged potassium ions of kinetic…

QPages 230-234: Q42: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q42 Solution: A narrow beam of singly charged potassium ions of kinetic…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the two isotopes as having the same speed because they share the same kinetic energy. In fact, $K=rac12 m v^2$ gives $v=sqrt{2K/m}$, so the heavier isotope moves more slowly. Since the radius in a magnetic field is $r=rac{m v}{qB}$, the radius actually scales as $sqrt{m}$, not linearly with $m$. Compute $v$ separately for each isotope before finding $r$, the deflection angle, and the final separation.

A narrow beam of singly charged potassium ions of kinetic energy 32 keV is injected into a region of width 1.00 cm with a magnetic field of strength 0.500 T, as shown in the figure. The ions are collected at a screen 95.5 cm away from the field region. If the beam contains isotopes of atomic weights 39 and 41, find the separation between the points where these isotopes strike the screen. Take the mass of a potassium ion =

A1.6 \times 10^{-27}) \text{ kg}

, where

A

is the mass number.

Step-by-Step Verified Solution

**Answer:** Separation

= 1.14 \text{ cm}

. **Step-by-Step Explanation:** The ions are deflected in the magnetic field and then travel in straight lines to the screen. The separation is determined by the difference in radii for the two isotopes.

QPages 230-234: Q42: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q42 Solution: A narrow beam of singly charged potassium ions of kinetic…

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