Question

If a hydrogen atom and a helium atom have the same kinetic energy:________

Answer 1

Answer: If a hydrogen atom and a helium atom have the same kinetic energy then the wavelength of the hydrogen atom will be roughly equal to the wavelength of the helium atom.

Explanation:

The relation between energy and wavelength is as follows.

$E = \frac{hc}{\lambda}$

This means that energy is inversely proportional to wavelength.

As it is given that energy of a hydrogen atom and a helium atom is same.

Let us assume that $E_{hydrogen} = E_{helium} = E'$. Hence, relation between their wavelengths will be calculated as follows.

$E_{hydrogen} = \frac{hc}{\lambda_{hydrogen}}$    ... (1)

$E_{helium} = \frac{hc}{\lambda_{helium}}$         ... (2)

Equating the equations (1) and (2) as follows.

$E_{hydrogen} = E_{helium} = E'\\\frac{hc}{\lambda_{hydrogen}} = \frac{hc}{\lambda_{helium}} = E'\\\lambda_{helium} = \lambda_{hydrogen} = E'$

Thus, we can conclude that if a hydrogen atom and a helium atom have the same kinetic energy then the wavelength of the hydrogen atom will be roughly equal to the wavelength of the helium atom.