a large number of hydrogen atoms have electrons excited to the n_h=4 state.How many possible spectral lines can appear in the emission spectrum as a results of the electron reaching the ground state(n_1=1)?
I count 6.
4 to 1
4 to 2
4 to 3
3 to 2
3 to 1
2 to 1
You might want to draw out the levels and make sure that's all.
200
To determine the number of possible spectral lines that can appear in the emission spectrum when hydrogen atoms have electrons excited to the n_h = 4 state and then drop back to the ground state (n_1 = 1), we need to use the formula for the number of possible transitions between two energy levels.
The formula is given by:
n = (n_h^2) - (n_1^2)
where:
n_h is the higher energy level (4 in this case, n_h = 4)
n_1 is the lower energy level (1 in this case, n_1 = 1)
n is the number of possible spectral lines
Plugging the values into the formula, we have:
n = (4^2) - (1^2)
n = 16 - 1
n = 15
Therefore, there are 15 possible spectral lines that can appear in the emission spectrum as a result of the electron reaching the ground state (n_1 = 1) from the excited state (n_h = 4).