Calculate the energy associated with the photon that would be released when an H electron falls fro the n=3 energy level to the n=1 energy level. show work if possible so I can understand how to do it. Thanks in advance!!!
I can't type this in the format you want because the site won't handle it. So n1 will be a and n2 will be b.
1/wavelength = R(1/a^2 - 1/b^2)
n1 = a = 1. 1^2 = 1
n2 = b = 3. b^2 = 9
1/wavelength = R(1/1 - 1/9).
R = 1.0973E7
wavelength will be in meters.
Then E = hc/wavelength
To calculate the energy associated with the photon released when an electron falls from one energy level to another, you can use the equation:
ΔE = hf
where ΔE is the change in energy, h is Planck's constant (6.626 x 10^-34 Js), and f is the frequency of the photon.
Since energy is inversely proportional to the wavelength of the photon, you can also use the equation:
E = hc/λ
where E is the energy, h is Planck's constant, c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength of the photon.
Now, to calculate the energy associated with the electron transition from the n=3 to the n=1 energy level in a hydrogen atom, we can use the Bohr's equation:
1/λ = R_H (1/n_final^2 - 1/n_initial^2)
where λ is the wavelength, R_H is the Rydberg constant (1.097 x 10^7 m^-1), n_final is the final energy level, and n_initial is the initial energy level.
In this case, n_initial = 3 and n_final = 1. Let's plug in these values and calculate the wavelength:
1/λ = R_H (1/1^2 - 1/3^2)
1/λ = R_H (1 - 1/9)
1/λ = R_H (8/9)
λ = 9/8 R_H
Having obtained the wavelength, we can now use the equation E = hc/λ to calculate the energy of the photon:
E = hc/λ
E = (6.626 x 10^-34 Js) x (3.0 x 10^8 m/s) / (9/8 R_H)
E = (6.626 x 10^-34 x 3.0 x 10^8 x 8) / (9 R_H)
E = (15.774 x 10^-26) / (9 R_H)
E = 1.752 x 10^-26 / (R_H)
Now we need to substitute the value of R_H:
E = 1.752 x 10^-26 / (1.097 x 10^7 m^-1)
E = 1.595 x 10^-33 J
Therefore, the energy associated with the photon released when an electron falls from the n=3 energy level to the n=1 energy level is approximately 1.595 x 10^-33 J.
Note: While this calculation provides an approximate value, it highlights the concept and method of calculating energy differences associated with electron transitions in hydrogen.