For the following electronic transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation.
From n = 3 to n = 6.
From n = 9 to n = 3.
From n = 7 to n = 4.
I will be happy to critique, repost with how you approach it.
To calculate the energy, frequency, and wavelength of the associated radiation for the electronic transitions in the hydrogen atom, we can use the following formulas:
1. Energy (E) of a transition can be calculated using the formula:
E = -13.6 eV / (n^2)
Where n represents the principal quantum number of the electron's initial or final orbit.
2. Frequency (ν) of the radiation can be calculated using the formula:
ν = E / h
Where E represents the energy of the transition and h is Planck's constant (6.626 x 10^-34 J·s).
3. Wavelength (λ) of the radiation can be calculated using the formula:
λ = c / ν
Where c is the speed of light (3.00 x 10^8 m/s) and ν represents the frequency of the radiation.
Now, let's calculate the energy, frequency, and wavelength for each transition:
1. From n = 3 to n = 6:
Energy:
E = -13.6 eV / (3^2) = -13.6 eV / 9 = -1.51 eV
Frequency:
ν = (-1.51 eV) / (6.626 x 10^-34 J·s) = -2.28 x 10^15 Hz
Wavelength:
λ = (3.00 x 10^8 m/s) / (-2.28 x 10^15 Hz) = 1.32 x 10^-7 m
2. From n = 9 to n = 3:
Energy:
E = -13.6 eV / (9^2) = -13.6 eV / 81 = -0.168 eV
Frequency:
ν = (-0.168 eV) / (6.626 x 10^-34 J·s) = -2.54 x 10^14 Hz
Wavelength:
λ = (3.00 x 10^8 m/s) / (-2.54 x 10^14 Hz) = 1.18 x 10^-6 m
3. From n = 7 to n = 4:
Energy:
E = -13.6 eV / (7^2) = -13.6 eV / 49 = -0.278 eV
Frequency:
ν = (-0.278 eV) / (6.626 x 10^-34 J·s) = -4.20 x 10^14 Hz
Wavelength:
λ = (3.00 x 10^8 m/s) / (-4.20 x 10^14 Hz) = 7.14 x 10^-7 m
Therefore, the calculated energy, frequency, and wavelength for the given electronic transitions are as follows:
1. From n = 3 to n = 6:
Energy = -1.51 eV, Frequency = -2.28 x 10^15 Hz, Wavelength = 1.32 x 10^-7 m
2. From n = 9 to n = 3:
Energy = -0.168 eV, Frequency = -2.54 x 10^14 Hz, Wavelength = 1.18 x 10^-6 m
3. From n = 7 to n = 4:
Energy = -0.278 eV, Frequency = -4.20 x 10^14 Hz, Wavelength = 7.14 x 10^-7 m