An electron in an hydrogen atom makes a transition from the ground state, #n=1#, to the excited state, #n=5#. Calculate the energy in Joules, frequency in Hertz #(1/s)#, and wavelength in #nm# of the photon?
1 Answer
The energy, frequency, and wavelength are, respectively,
Explanation:
Wavelength
You use the Rydberg formula to calculate the wavelength, λ:
#color(blue)(bar(ul(|color(white)(a/a) 1/λ = RZ^2(1/n_2^2 -1/n_1^2)color(white)(a/a)|)))" "#
where
In this problem,
The negative sign shows that energy is absorbed.
Frequency
The formula relating frequency
#color(blue)(bar(ul(|color(white)(a/a)fλ = c color(white)(a/a)|)))" "#
where
We can rearrange the formula to get
#f = c/λ#
∴
The formula relating energy
#color(blue)(bar(ul(|color(white)(a/a)E = hfcolor(white)(a/a)|)))" "#
where
∴