A proton, a deuteron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :
- \(1 : \sqrt2 : \sqrt2\)
- \(1 : 1 : \sqrt2\)
- \(\sqrt2 : 1 : 1\)
- \(1 : \sqrt2 : 1\)
The Correct Option is D
Solution and Explanation
∴ \(r = \frac{mv}{qB}\)
= \(\frac{\sqrt{2m(KE)}}{qB}\)
\(r_1: r_2: r_3 = \frac{\sqrt m_1}{q_1} : \frac{\sqrt m_2}{q_2} : \frac{\sqrt m_3}{q_3}\)
= \(\frac{\sqrt 1}{1}:\frac{\sqrt 2}{1}:\frac{\sqrt 4}{2}\)
= \(1: \sqrt2 : 1\)
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
