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.

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