Frequency of the series limit of Balmer series of hydrogen atom

The Balmer series is a spectral line series of the hydrogen atom that corresponds to transitions between the second and higher energy levels to the first energy level.

The series limit of the Balmer series is the wavelength of the longest wavelength line in the series, which corresponds to the transition from the second energy level to the first energy level.

The frequency of the series limit of the Balmer series can be calculated using the formula:

ν = R(1/2^2 - 1/n^2)

where ν is the frequency of the series limit, R is the Rydberg constant, and n is the principal quantum number of the level of the hydrogen atom from which the electron is transitioning.

In this case, n = 2, so the formula becomes:

ν = R(1/4 - 1/n^2)

ν = R(1/4 - 1/4)

ν = R(0)

ν = 0

Therefore, the frequency of the series limit of the Balmer series is zero.

Frequency in terms of Rydberg constant R and velocity of light C

The frequency of the series limit of the Balmer series can also be expressed in terms of the Rydberg constant R and the velocity of light C using the formula:

λ = C/ν

where λ is the wavelength of the series limit, C is the velocity of light, and ν is the frequency of the series limit.

Rearranging the formula, we get:

ν = C/λ

Substituting the value of λ as the series limit wavelength for the Balmer series, we get:

ν = C/λ_limit

where λ_limit is the wavelength of the series limit for the Balmer series.

Using the formula for the series limit wavelength for the Balmer series:

λ_limit = R(1/2^2 - 1/∞^2)

λ_limit = R(1/4 - 0)

λ_limit = R/4

Substituting this value into the equation for frequency, we get:

ν = C/(R/4)

ν = 4C/R

Therefore, the frequency of the series limit of the Balmer series in terms of the Rydberg constant R and the velocity of light C is 4C/R, which is option B.