Question

A particle is projected horizontally with a velocity $10m/s$. What will be the ratio of de-Broglie wavelengths of the particle, when the velocity vector makes an angle ${30}^{\circ }$ and ${60}^{\circ }$ with the horizontal?

• A. $\sqrt{3}:1$
• B. $1:\sqrt{3}$
• C. $2:\sqrt{3}$
• D. $\sqrt{3}:2$

Answer 1

The correct option is A $\sqrt{3}:1$

Given:-$V_1=10m/s$

Solution:-

Velocity when velocity vector makes ${30}^o$ with

horizontal,$V_2=V_1\times \cos {30}^o$

$=V_1\times \frac{\sqrt{3}}{2}$

$V_2=\frac{10\sqrt{3}}{2}=5\sqrt{3}m/s$

Velocity when velocity vector makes ${60}^o$ with

horizontal,$V_3=V_1\cos {60}^o$

$V_3=V_1\times \frac{1}{2}$

$V_3=10\times \frac{1}{2}$

$V_3=5m/s$

$\therefore$ Ratio of wavelength is:-

$\sqrt{3}:1$