Respuesta :
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.
[tex]E = \frac{hc}{\lambda}\\[/tex]
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 [tex]E_{hydrogen} = E_{helium} = E'[/tex]. Hence, relation between their wavelengths will be calculated as follows.
[tex]E_{hydrogen} = \frac{hc}{\lambda_{hydrogen}}[/tex] ... (1)
[tex]E_{helium} = \frac{hc}{\lambda_{helium}}[/tex] ... (2)
Equating the equations (1) and (2) as follows.
[tex]E_{hydrogen} = E_{helium} = E'\\\frac{hc}{\lambda_{hydrogen}} = \frac{hc}{\lambda_{helium}} = E'\\\lambda_{helium} = \lambda_{hydrogen} = E'[/tex]
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.
