Question:

The longest wavelength line in the Lyman series of the hydrogen spectrum is

Updated On: Jan 26, 2024
  • 949.8? 949.8\,?
  • 972.6? 972.6\,?
  • 1215.8? 1215.8\,?
  • 1025.8? 1025.8\,?
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The Correct Option is C

Solution and Explanation

1λRH[1n121n22]\frac{1}{\lambda} R_{H}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]
For longest wavelength in Lyman series,
n1=1,n2=2n_{1}=1, n_{2}=2
1λ=1.09678×107[1(1)21(2)2]\frac{1}{\lambda}=1.09678 \times 10^{7}\left[\frac{1}{(1)^{2}}-\frac{1}{(2)^{2}}\right]
1λ=1.09678×107×34\frac{1}{\lambda}=\frac{1.09678 \times 10^{7} \times 3}{4}
λ=1.2156×107m\therefore \lambda=1.2156 \times 10^{-7} \,m
=1215.6?=1215.6\,?
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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.

1λ=RZ2(1n121n22)\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.