If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is _______ nm. (Nearest integer)

The Paschen series in the hydrogen spectrum corresponds to transitions from higher energy levels to the n=3 level.

The wavelength of the lines in the Paschen series can be calculated using the formula for the hydrogen emission spectrum:

1/λ = R * (1/n1² - 1/n2²)

where:

• λ is the wavelength
• R is the Rydberg constant (approximately 1.097 x 10^7 m^-1)
• n1 and n2 are the energy levels of the electron before and after the transition (with n1 < n2)

For the first line of the Paschen series, the electron transitions from the n=4 level to the n=3 level. Given that the wavelength of this line is 720 nm, we can use the formula to find the value of the Rydberg constant:

1/720 nm = R * (1/3² - 1/4²)

Solving for R gives us a value of approximately 1.097 x 10^7 m^-1, which is consistent with the known value of the Rydberg constant.

For the second line of the Paschen series, the electron transitions from the n=5 level to the n=3 level. We can use the formula again to find the wavelength of this line:

1/λ = R * (1/3² - 1/5²)

Solving for λ gives us a value of approximately 1282 nm. Rounding to the nearest integer, the wavelength of the second line of the Paschen series is 1282 nm.