What is the energy of light (in J) emitted by a hydrogen atom when an electron relaxes from the 7 energy level to the 5 energy level?
https://brilliant.org/wiki/energy-level-and-transition-of-electrons/
To calculate the energy of light emitted by a hydrogen atom when an electron transitions from one energy level to another, we can use the formula:
ΔE = E2 - E1
where ΔE represents the change in energy, and E2 and E1 are the energy levels the electron transitions from and to, respectively.
First, we need to find the energy values of the hydrogen atom for the given energy levels. The energy of a hydrogen atom can be determined using the Rydberg formula:
E = -13.6 eV / n^2
where E is the energy in electron volts (eV), and n is the principal quantum number representing the energy level.
For the initial energy level (n_i = 7):
E1 = -13.6 eV / (7^2)
For the final energy level (n_f = 5):
E2 = -13.6 eV / (5^2)
Next, we need to convert the energy values from electron volts (eV) to joules (J). The conversion factor is:
1 eV = 1.602 x 10^-19 J
Thus, we can multiply the energy values by the conversion factor to obtain the energy in joules.
Finally, we can calculate the energy of light (ΔE) emitted by the hydrogen atom during the electron transition:
ΔE = E2 - E1
Once you have the values for E1 and E2, simply subtract E1 from E2 to find ΔE.