Longest wavelength of Balmer series of H-atom is 6563 o A . Longest wavelength of Lyman series, will be

The Balmer and Lyman series are two different series of spectral lines corresponding to electronic transitions in the hydrogen atom. The Balmer series corresponds to transitions from higher energy levels to the second energy level, while the Lyman series corresponds to transitions to the first energy level.

The longest wavelength in the Balmer series corresponds to the smallest energy difference, which is the transition from the third to the second energy level. The wavelength of this transition is given as 6563 Angstroms.

The Rydberg formula can be used to calculate the wavelength of spectral lines in the hydrogen spectrum:

1/λ = R * (1/n1² - 1/n2²)

where R is the Rydberg constant (approximately 1.097373 x 10^7 m^-1), n1 and n2 are the initial and final energy levels (with n1 < n2), and λ is the wavelength.

For the longest wavelength in the Balmer series, n1 = 2 and n2 = 3. Plugging these values into the Rydberg formula gives:

1/λ = R * (1/2² - 1/3²)

Solving for λ gives λ = 6563 Angstroms.

For the longest wavelength in the Lyman series, the transition is from the second to the first energy level, so n1 = 1 and n2 = 2. Plugging these values into the Rydberg formula gives:

1/λ = R * (1/1² - 1/2²)

Solving for λ gives the longest wavelength in the Lyman series.