Number of Spectral Lines Emitted when an Electron is Excited to nth Energy State in Hydrogen
When an electron in a hydrogen atom is excited to the nth energy state, it can transition back to a lower energy state by emitting a photon. The number of spectral lines emitted in this process depends on the specific energy levels involved.

Determination of Spectral Lines
1. Single Transition: If the electron transitions directly from the nth energy state to the ground state (n=1), only one spectral line is emitted. This is known as a single transition.
2. Multiple Transitions: If the electron transitions through intermediate energy levels before reaching the ground state, multiple spectral lines are emitted. Each transition corresponds to a specific wavelength of light, resulting in a series of spectral lines.

Formula for Spectral Lines
The total number of spectral lines emitted can be calculated using the formula:
\[ \text{Number of Spectral Lines} = n^2 - n \]
where 'n' represents the energy level to which the electron is excited. This formula takes into account all possible transitions back to lower energy levels.

Example
For instance, if the electron is excited to the 3rd energy state (n=3), the number of spectral lines emitted would be:
\[ 3^2 - 3 = 6 \]
Therefore, in this scenario, a total of 6 spectral lines would be observed as the electron transitions back to lower energy levels.
In conclusion, the number of spectral lines emitted when an electron is excited to the nth energy state in hydrogen can vary depending on the specific energy levels involved and can be determined using the formula mentioned above.

(n2-n1)(n2-n1plus1)/2 but ifn-1 then n(n-)/2