Explanation:

Balmer series is the set of spectral lines produced by the hydrogen atom when the electron jumps from higher energy levels to the second energy level.

The Balmer series is given by the formula:

1/λ = Rh [ (1/2^2) - (1/n^2) ]

where λ is the wavelength of the spectral line, Rh is the Rydberg constant, and n is the principal quantum number of the higher energy level.

The third line in the Balmer series corresponds to the transition from the fourth energy level (n=4) to the second energy level (n=2).

Bohr's model of the hydrogen atom states that the electron in the hydrogen atom can exist only in certain discrete energy levels. The electron can move from one energy level to another by absorbing or emitting energy in the form of electromagnetic radiation.

The energy of the electron in the nth energy level is given by the formula:

E = - (13.6/n^2) eV

where n is the principal quantum number.

Therefore, the energy difference between the fourth energy level and the second energy level is:

ΔE = E4 - E2 = - (13.6/4^2) + (13.6/2^2) = 10.2 eV

The energy of a photon with a wavelength of the third line in the Balmer series is:

E = hc/λ = (6.626 x 10^-34 J.s) x (3 x 10^8 m/s) / (656.3 x 10^-9 m) = 3.02 eV

Since ΔE = E, we can equate the two equations and find the value of n:

ΔE = E = 10.2 eV = - (13.6/n^2) eV

n^2 = 4

n = 2 or -2

Since the principal quantum number cannot be negative, the correct answer is option B, which corresponds to the transition from the fifth energy level (n=5) to the second energy level (n=2).

B)

5 → 2