Question

Assume that a hydrogen atom's electron has been excited to the n ???? 5 level. how many different wavelengths of light can be emitted as this excited atom loses energy?

Answer 1

From n = 5, the electron can drop to n = 4, 3, 2, 1 . Thus, there will be 4 possibilities

Now, the electron that dropped to n = 4 can drop to n = 3, 2, 1. This will give 3 possibilities

The electron at n = 3, can drop to n = 2, 1. This gives 2 possibilities

Finally, the electron at n = 2 can drop to n=1. This gives 1 possibility

Thus in total the number of ways in which the electron can de-excite is :

4+3+2+1 = 10

10 different wavelengths of light can be emitted as the electron loses energy from n = 5 level

Answer 2

n = 5 --> n = 4

n = 4 --> n = 3

n = 3 --> n = 2

n = 2 --> n = 1

So we can see that there are 4 different wavelength of light that can be emitted