Question

what isthe maximum number of spectral lines emitted by a hydrogen atom when it is in the third excited state​

Answer 1

Max number of Spectral lines = 6

Explanation:

If n is the quantum number of highest energy level, then the total number of possible spectral line emitted is  N = n(n - 1) / 2.

The question is about the spectral lines emitted in third excited state hydrogen. Then n = 4 as it is the fourth energy level of hydrogen.

The number of possible spectral lines N = 4 (4-1) /2 = 2 * 3 = 6

Answer 2

Number of spectral lines when hydrogen electron jump from third excited state to its ground state is 6.

We known by the formula that number of spectral lines are given by

=> (n2-n1)(n2-n1+1)/2

Where n1 is the ground state n1 = 1

And n2 is the excited state where electron is present for this case n2 = 4

When n1 = 1 the formula is modified as n(n- 1)/2......(1)

Where n is the excited state so n= 4

Substituting values in equation (1) we have:--

=> 4(4-1)/2

=>4*3/2 = 2*3 = 6

So, maximum number of spectral lines emitted by a hydrogen atom when it is in the third excited state​(n2=4) are 6.