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Karnataka Board PUCPUC Science 2nd PUC Class 12
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The Line Spectra of the Hydrogen Atom

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Estimated time: 6 minutes
CBSE: Class 12

Introduction

According to the third postulate of Bohr’s model, when an atom transitions from a higher energy state with quantum number ni to a lower energy state with quantum number nf, where nf < ni, the energy difference is carried away by a photon of frequency νif.

The relation is:

hνif = Eni − Enf

This shows that when an electron transitions from a higher to a lower energy state, radiation is emitted as a photon.

CBSE: Class 12

History/Origin

The explanation of the hydrogen atom spectrum given by Bohr’s model was a brilliant achievement and greatly stimulated progress toward modern quantum theory. Bohr was awarded the Nobel Prize in Physics in 1922.

CBSE: Class 12

Definition: Emission Lines

The various lines in atomic spectra are produced when electrons jump from a higher energy state to a lower energy state, and photons are emitted. These spectral lines are called emission lines.

OR

Emission lines are the spectral lines produced when electrons fall from higher energy states to lower energy states and emit photons.

CBSE: Class 12

Definition: Absorption

When an atom absorbs a photon having precisely the same energy as that required for an electron in a lower energy state to make a transition to a higher energy state, the process is called absorption.

OR

Absorption is the process in which an atom takes in a photon whose energy exactly matches the energy needed for an electronic transition from a lower level to a higher level.

CBSE: Class 12

Definition: Absorption Spectrum

Dark spectral absorption lines are the lines seen in a continuous spectrum at the frequencies absorbed by the atoms of a rarefied gas.

CBSE: Class 12

Key Points: The Line Spectra of the Hydrogen Atom

  • An atom emits radiation when it moves from a higher energy state to a lower energy state.
  • The energy difference appears as a photon.
  • Because the quantum numbers are integers, only discrete frequencies are emitted.
  • These give rise to emission lines.
  • If atoms absorb photons of the exact required energy, dark absorption lines appear in a continuous spectrum.

Related QuestionsVIEW ALL [44]

Find the binding energy of a hydrogen atom in the state n = 2.

Let En = `(-1)/(8ε_0^2) (me^4)/(n^2h^2)` be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency (E2 - E1)/h falls on it ______.

  1. it will not be absorbed at all.
  2. some of atoms will move to the first excited state.
  3. all atoms will be excited to the n = 2 state.
  4. no atoms will make a transition to the n = 3 state.

Find the temperature at which the average thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state to n = 3 state. Hydrogen can now emit red light of wavelength 653.1 nm. Because of Maxwellian distribution of speeds, a hydrogen sample emits red light at temperatures much lower than that obtained from this problem. Assume that hydrogen molecules dissociate into atoms.

Calculate the smallest wavelength of radiation that may be emitted by (a) hydrogen, (b) He+ and (c) Li++.

Which wavelengths will be emitted by a sample of atomic hydrogen gas (in ground state) if electrons of energy 12.2 eV collide with the atoms of the gas?

Average lifetime of a hydrogen atom excited to n = 2 state is 10−8 s. Find the number of revolutions made by the electron on the average before it jumps to the ground state.

When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed in Lyman series only. Explain.

What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state?

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