Given information:
The frequency of one of the lines in the Paschen series of the hydrogen atom is 2.340×10^14 Hz.

To find:
The quantum number (n2) which produces this transition.

Explanation:

Paschen series:
The Paschen series is a series of spectral lines in the hydrogen atom that corresponds to transitions between the energy levels of the electron in the atom. It occurs when the electron transitions from a higher energy level to the third energy level (n=3).

Formula:
The frequency of a spectral line can be determined using the Rydberg formula:
1/λ = R [1/n1^2 - 1/n2^2]
Where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels, respectively.

Steps to solve the problem:

1. Convert the given frequency into wavelength using the formula:
c = λν
Where c is the speed of light (3 x 10^8 m/s), λ is the wavelength, and ν is the frequency.

2. Substitute the wavelength value in the Rydberg formula to find the initial energy level (n1) for the Paschen series.

3. The final energy level (n2) for the Paschen series is always 3.

4. Solve the Rydberg formula for n2.

5. Compare the value of n2 obtained from the calculation with the given options (A, B, C, D) and select the correct option.

Calculation:

1. Wavelength:
c = λν
λ = c/ν
λ = (3 x 10^8 m/s) / (2.340 x 10^14 Hz)
λ ≈ 1.282 x 10^-6 m

2. Rydberg formula:
1/λ = R [1/n1^2 - 1/n2^2]
Substituting λ = 1.282 x 10^-6 m and n2 = 3:
1/(1.282 x 10^-6) = R [1/n1^2 - 1/3^2]
n1^2 = (9/8) x (1.282 x 10^-6)
n1^2 ≈ 1.153 x 10^-6
n1 ≈ √(1.153 x 10^-6)
n1 ≈ 0.0011

3. The final energy level (n2) for the Paschen series is always 3.

4. Comparing the value of n2 obtained from the calculation (n2 = 3) with the given options (A, B, C, D), we find that option B is the correct answer.

Therefore, the quantum number (n2) which produces this transition is B) 5.

For the paschen series n2 is 5