Question

The velocities of two particles A and Bare 0.05 and 0.02 m$s^{-1}$ respectively. The mass of B is five times the mass of A. The ratio of their de-Broglie wavelength is:

• A. $2:1$
• B. $-1:4$
• C. $1:1$
• D. $4:1$

Answer 1

The correct option is A $2:1$

Given, velocity of particle $A=0.05{ms}^{-1}$
Velocity of particle $B=0.02{ms}^{-1}$
Let the mass of particle $A=x$
$\therefore$ The mass of particle $B=5x$
de-Broglie's equation is
$\lambda =\frac{h}{mv}$
For particle $A$
${\lambda }_A=\frac{h}{x\times 0.05}$ ....(i)
For particle $B$
$\lambda =\frac{h}{5x\times 0.02}$ .....(ii)
Equation (i) / (ii)
$\frac{{\lambda }_A}{{\lambda }_B}=\frac{5x\times 0.02}{x\times 0.05}$
$\frac{{\lambda }_A}{{\lambda }_B}=\frac{2}{1}$
Or $2:1$