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Karnataka Board PUCPUC Science 2nd PUC Class 12

Energy Levels

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Estimated time: 6 minutes
CBSE: Class 12

Introduction

The energy of the electron in a hydrogen atom has a definite value in each allowed orbit. The energy of the electron in the innermost orbit is the lowest. This state is called the ground state.

For hydrogen atom, the energy of the electron in the first orbit is:

E1 = −13.6 eV

This means that 13.6 eV of energy must be supplied to remove the electron completely from the atom in its ground state. This energy is called the ionisation energy of hydrogen. 

CBSE: Class 12

Excited States

When a hydrogen atom absorbs energy, its electron can jump from the ground state to a higher orbit. Such a state is called an excited state.

If the electron jumps to the second orbit, the energy of the atom becomes:

E2 = −3.40 eV

Therefore, the energy required to raise the atom from the ground state to the first excited state is:

E2 − E1 = (−3.40) − (−13.6) = 10.2 eV

If the electron jumps to the third orbit, the energy of the atom is:

E3 = −1.51 eV

So, the energy required to raise the atom from the ground state to the second excited state is:

E3 − E1 = (−1.51) − (−13.6) = 12.09 eV
CBSE: Class 12

Energy States of the Hydrogen Atom

  • The ground state corresponds to the lowest energy of the atom.
  • The energy of the electron in a hydrogen atom is negative in bound states.
  • As the orbit number increases, the energy becomes less negative.
  • The energy required to remove an electron from an excited state is less than that required to remove an electron from the ground state.
  • When the electron is completely free from the atom, its energy is taken as zero.
CBSE: Class 12

Energy Values

Orbit State Energy
n = 1 Ground state -13.6 eV 
n = 2 First excited state -3.40 eV 
n = 3 Second excited state -1.51 eV 
n = ∞ Free electron 0 eV 
CBSE: Class 12

Key Points: Energy Levels

  • Ground state energy of hydrogen = -13.6 eV.
  • Ionisation energy of hydrogen in the ground state = 13.6 eV.
  • Energy required for first excitation = 10.2 eV.
  • Energy required for second excitation = 12.09 eV.
  • The energy of a free electron is 0 eV.

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