Question

Two particles A and B are in motion. If the wavelength associated with particle A is $5\times {10}^{-8}m$; Calculate the wavelength associated with particle B if momentum is half of A.

Answer 1

The relation between wavelength and momentum of moving particle is given by
Momentum $=\frac{h}{wavelength}$
$p=\frac{h}{\lambda }$
Wavelength of the particle $A=5\times {10}^{-8}m$
Let the momentum of particle A is $p_A$ and the momentum of the particle B is pB
Relation between $p_A$ and $p_B$ is:
$p_B=\frac{p_A}{2}$
$p_A=\frac{h}{5}\times {10}^{-8}m$
$p_B=\frac{h}{5}\times {10}^{-8}m\times 2$
Wavelength of B(lambda)
$=\frac{h}{p_B}=\frac{h}{\frac{h}{5}}\times {10}^{-8}m\times 2=10\times {10}^{-8}m={10}^{-7}m$