Question

Calculate the linear momentum of photons of wavelength 350 nm. What speed does a hydrogen molecule need to travel to have the same linear momentum?

Answer 1

Answer:

a)$p=1.89x10^{-27}kg.m.s^{-1}$

b)$v=0.565\frac{m}{s}$

Explanation:

First, we need to obtain the linear momentum of the photons of wavelength 350nm.

We are going to use the following formula:

$\lambda=\frac{h}{p}\\Where:\\\lambda=wavelength\\h=placnk's\_constant\\p=Linear\_momentum$

So the linear momentum is given by:

$p=\frac{h}{\lambda}\\\\p=\frac{6.626x10^{-34}J.s}{350x10^{-9}m}\\\\p=1.89x10^{-27}kg.m.s^{-1}$

Having the linear momentum of the photon, we can calculate the speed of the hydrogen molecule to have the same momentum, we can use the classic formula for that:

$p=m.v$

$where:\\m=mass\\v=speed\\p=linear\_momentum$

The mass of the hydrogen molecule is given by:

$m=2*(1.0078x10^{-3}\frac{kg}{mol}})x\frac{1}{6.022x10^{23}mol}$

$3.35x10^{-27}kg$

What we've done here is to use the molecular weight of the hydrogen, and covert it kilograms, we had to multiply by two because the hydrogen molecule is found in pairs.

so:

$v=\frac{p}{m}\\\\v=\frac{1.89x10^{-27}kg.m.s^{-1}}{3.35x10^{-27}kg}\\\\v=0.565\frac{m}{s}$