If the electron jumps from n2 = 5 to n1 = 1 then following are the transitions possible. Hence there are 10 transitions and hence 10 spectral lines possible.

Expression to Calculate the Wave Number of Spectral Line in the Hydrogen Spectrum

The wave number of a spectral line in the hydrogen spectrum can be calculated using the following expression:

Wave Number (ν) = 1 / Wavelength (λ)

Explanation:

1. Spectral Lines in the Hydrogen Spectrum:
The hydrogen spectrum is a series of lines observed in the emission or absorption of light by hydrogen atoms. These lines correspond to different energy transitions that occur within the hydrogen atom when its electrons move between different energy levels.

2. Wave Number:
The wave number (ν) represents the number of waves per unit distance. It is defined as the reciprocal of the wavelength (λ) of a wave. The wave number is usually expressed in units of reciprocal meters (m⁻¹) or reciprocal centimeters (cm⁻¹).

3. Relationship between Wave Number and Wavelength:
The wavelength (λ) and wave number (ν) are inversely proportional to each other. This means that as the wavelength of a wave decreases, the wave number increases, and vice versa. Mathematically, this relationship can be expressed as:

ν = 1 / λ

This expression allows us to calculate the wave number of a spectral line in the hydrogen spectrum when the wavelength is known.

4. Calculation Example:
Let's consider an example where the wavelength (λ) of a spectral line in the hydrogen spectrum is given as 656.3 nm (nanometers).

To calculate the wave number, we can use the expression:

ν = 1 / λ = 1 / 656.3 nm

First, we need to convert the wavelength from nanometers to meters by dividing by 10⁹:

ν = 1 / (656.3 nm / 10⁹) m⁻¹

Next, we simplify the expression:

ν = 10⁹ / 656.3 m⁻¹

Finally, we calculate the wave number:

ν ≈ 1.521 × 10⁶ m⁻¹

Therefore, the wave number of the spectral line in the hydrogen spectrum with a wavelength of 656.3 nm is approximately 1.521 × 10⁶ m⁻¹.

Conclusion:

The expression to calculate the wave number of a spectral line in the hydrogen spectrum is ν = 1 / λ, where ν represents the wave number and λ represents the wavelength. This expression allows us to determine the number of waves per unit distance for a given wavelength. By using this expression, we can easily convert between wavelength and wave number in the hydrogen spectrum.

Wave no. = R[1/n1^2 - 1/n2^2].where, R is Rydberg constant.N1 and N2 is the no. of spectral line.