Question

A particle of mass M at rest decays into two particles of masses $m_1 \, and \, \, m_2$ having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles $\frac{\lambda_1}{\lambda_2}$ is

• A. $m_1/m_2$
• B. $m_2/m_1$
• C. 1
• D. $\sqrt{m_2}/\sqrt{m_1}$

Answer 1

Answer: (C)

1

Answer 2

From law of conservation of momentum, $P_1 = P_2$ (in opposite directions) Now de-Broglie wavelength is given by $\, \, \lambda = \frac{h}{p},$ where h = Planck's constant Since magnitude of momentum (p) of both the particles is equal, therefore $\lambda_1 = \lambda_2$ or $\lambda_1/ \lambda_2 = 1$