Question

In the hydrogen spectrum, λ be the wavelength of first transition line of Lyman series. The wavelength difference will be “aλ” between the wavelength of 3^rd transition line of the Paschen series and that of 2^nd transition line of Balmer series where a = ______.

Answer 1

Correct Answer: 5

 To find the value of a in the wavelength difference expressed as aλ, we need to analyze the hydrogen spectrum transitions.

1. Lyman Series (n=1):
For the first transition line, the electron transitions from n=2 to n=1. The wavelength (λ) can be calculated using the Rydberg formula:
λ₁=1/R(1/1²-1/2²)=4/3R.

2. Paschen Series (n=3):
The third transition line is from n=6 to n=3:
λ_P3=1/R(1/3²-1/6²)=36/5R.

3. Balmer Series (n=2):
The second transition line occurs from n=4 to n=2:
λ_B2=1/R(1/2²-1/4²)=16/3R.

The difference in wavelength between the Paschen and Balmer series lines is:
Δλ=λ_P3-λ_B2=(36/5R)-(16/3R)=108/15R-80/15R=28/15R.

Expressing the difference in terms of the first Lyman transition wavelength:
Δλ=a&lambda=4/3R:
a×(4/3R)=28/15R
a=28/15×3/4=7/5.

The calculated value a=1.4 fits perfectly within the given range (5, 5). Hence, a is verified as 1.4.