When the electron in a hydrogen atom moves from n = 5 to n = 1, light is emitted.
Calculate the energy of the light?
delta E in joules = 2.180 E-18[1/(n1)^2 - 1/(n2)^2]
n1 = 1
n2 = 5
To calculate the energy of the light emitted when an electron in a hydrogen atom moves from one energy level to another, we use the equation:
ΔE = E_final - E_initial
where ΔE is the change in energy, E_final is the energy of the final state, and E_initial is the energy of the initial state.
In the hydrogen atom, the energy levels are given by the equation:
E = -13.6 * (Z^2 / n^2) eV,
where Z is the atomic number (which is 1 for hydrogen) and n is the principal quantum number.
In this case, the electron is moving from n = 5 to n = 1. Let's calculate the energy:
E_final = -13.6 * (1^2 / 1^2) eV = -13.6 eV
E_initial = -13.6 * (1^2 / 5^2) eV = -13.6 * (1/25) eV = -0.544 eV
Now we can calculate the change in energy:
ΔE = E_final - E_initial
= (-13.6 eV) - (-0.544 eV)
= -13.056 eV
The energy of the light emitted is equal to the absolute value of the change in energy:
Energy of the light = |ΔE|
= |-13.056 eV|
= 13.056 eV
Therefore, the energy of the light emitted when the electron in a hydrogen atom moves from n = 5 to n = 1 is 13.056 eV.