The wavelength of first line of balmer series in hydrogen spectrum is 6563 A. Find the wavelength of first line of lyman series in the same spectrum.
1215.4
To find the wavelength of the first line of the Lyman series in the hydrogen spectrum, we can use the Rydberg formula. The Rydberg formula provides a mathematical relationship between the wavelength of the spectral lines and the energy levels in an atom.
The general formula is given by:
1/λ = R * (1/n_1^2 - 1/n_2^2)
Where:
- λ represents the wavelength of the spectral line
- R is the Rydberg constant (approximately 1.097 x 10^7 per meter)
- n_1 and n_2 are positive integers representing the initial and final energy levels, respectively
In this case, we are looking for the wavelength of the first line of the Lyman series. The Lyman series corresponds to the transition from the higher energy levels (n > 1) to the first energy level (n = 1). Therefore, we can set n_1 = 1 and n_2 = 2 in the Rydberg formula.
1/λ = R * (1/1^2 - 1/2^2)
1/λ = R * (1/1 - 1/4)
1/λ = R * (3/4 - 1/4)
1/λ = R * (2/4)
1/λ = R/2
Now, we can substitute the value of R (Rydberg constant) into the equation:
1/λ = 1.097 x 10^7 / 2
1/λ = 5.485 x 10^6 per meter
To convert this to angstroms (A), we need to divide it by 10 (1 meter = 10 angstroms).
Therefore:
1/λ = 5.485 x 10^6 / 10
1/λ = 5.485 x 10^5 A
So, the wavelength of the first line of the Lyman series in the hydrogen spectrum is approximately 5485 A.