Question

A particle of mass $4m$ at rest decays into two particles of masses $m$ and $3m$ having non-zero velocities. The ratio of the de Broglie wavelengths of the particles 1 and 2 is:

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $2$
• D. $1$

Answer 1

Answer: (D)

$1$

According to law of conservation of linear momentum, two particles will have equal and opposite momentum.
The de Broglie wavelength is given by

$\lambda =\frac{h}{p}\therefore \frac{{\lambda }_1}{{\lambda }_2}=1$