The electron in a hydrogen atom is excited and makes a transition from n=2 to n=7
a. calculate the energy of the photon absorbed in joules.
b. calculate the wavelength of the photon in meters
HOW DO I DO THIS?
1/wavelength = R(1/n1^2 - 1/n2^2)
R = Rydberg constant. I assume you have that in your text or notes.
For n1 you substitute 2 and square it.
For n2 substitute 7 and square it.
From wavelength, you can calculate energy from E = hc/wavelength.
(Note:I arranged n1 and n2 so you would get a positive number for wavelength. You must remember that you are going from 2 to 7 which means energy is absorbed.)
To calculate the energy of the photon absorbed in joules and the wavelength of the photon in meters for the given transition, you need to use the energy level equation and the equation for the energy of a photon.
a. To calculate the energy of the photon absorbed in joules, you can use the energy level equation:
E = -13.6 eV / n^2
Where E is the energy in electron volts (eV) and n is the principal quantum number of the energy level.
For the initial energy level (n=2), the energy is calculated as:
E1 = -13.6 eV / (2^2) = -13.6 eV / 4 = -3.4 eV
For the final energy level (n=7), the energy is calculated as:
E2 = -13.6 eV / (7^2) = -13.6 eV / 49 = -0.2776 eV
To convert the energy from electron volts to joules, you can use the conversion factor: 1 eV = 1.6 × 10^-19 J.
So, the energy change (ΔE) is:
ΔE = E2 - E1 = -0.2776 eV - (-3.4 eV) = 3.1224 eV
To convert this energy change to joules, use the conversion factor:
ΔE = 3.1224 eV × 1.6 × 10^-19 J/eV = 4.9958 × 10^-19 J
Therefore, the energy of the photon absorbed in joules is approximately 4.9958 × 10^-19 J.
b. To calculate the wavelength of the photon in meters, you can use the equation for the energy of a photon:
E = hc / λ
Where E is the energy of the photon, h is Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (3 × 10^8 m/s), and λ is the wavelength of the photon.
Rearranging the equation, we get:
λ = hc / E
Substituting the calculated energy change (ΔE) from part (a), we find:
λ = (6.626 × 10^-34 J·s × 3 × 10^8 m/s) / (4.9958 × 10^-19 J)
After evaluating this expression, you will find the wavelength of the photon in meters.
Please perform the calculations to obtain the final result for the wavelength.