The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number $Z$ of hydrogen like ion is

$\frac{1}{\lambda}= R Z^{2}\left(\frac{1}{ n _{1}^{2}}-\frac{1}{ n _{2}^{2}}\right)$ $R (1)^{2}\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)= R Z ^{2}\left(\frac{1}{2^{2}}-\frac{1}{4^{2}}\right)$ $Z =2$

The wavelength of light absorbed by Pr form of phytochrome is

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Concepts Used:

Atomic Spectra

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an electron making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states.

Read More: Atomic Spectra

Spectral Series of Hydrogen Atom

Rydberg Formula:

The Rydberg formula is the mathematical formula to compute the wavelength of light.

\[\frac{1}{\lambda} = RZ^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})\]

Where,

R is the Rydberg constant (1.09737*107 m-1)

Z is the atomic number

n is the upper energy level

n’ is the lower energy level

λ is the wavelength of light

Spectral series of single-electron atoms like hydrogen have Z = 1.

Uses of Atomic Spectroscopy:

It is used for identifying the spectral lines of materials used in metallurgy.
It is used in pharmaceutical industries to find the traces of materials used.
It can be used to study multidimensional elements.