Answer: The frequency of the green light emitted by a hydrogen atom with a wavelength of 546 nm is [tex]5.49 \times 10^{14} s^{-1}[/tex].
Explanation:
Given: Wavelength = 546 nm [tex](1 nm = 10^{-9} m)[/tex] = [tex]546 \times 10^{-9} m[/tex]
The relation between frequency and wavelength is as follows.
[tex]\nu = \frac{c}{\lambda}[/tex]
where,
[tex]\nu[/tex] = frequency
c = speed of light = [tex]3.0 \times 10^{8} m/s[/tex]
[tex]\lambda[/tex] = wavelength
Substitute the values into above formula as follows.
[tex]\nu = \frac{c}{\lambda}\\= \frac{3.0 \times 10^{8} m/s}{546 \times 10^{-9} m}\\= 5.49 \times 10^{14} s^{-1}[/tex]
Thus, we can conclude that the frequency of the green light emitted by a hydrogen atom with a wavelength of 546 nm is [tex]5.49 \times 10^{14} s^{-1}[/tex].
