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Potential energy

An electron possesses some potential energy because it is found in the field of nucleus potential energy of electron in nth orbit of radius rn is given by
 
102272.png

Kinetic energy

An electron possesses kinetic energy because of its motion. Closer orbits have greater kinetic energy than outer ones.
 
As we know 102278.png
 
⇒ Kinetic energy, 102284.png

Total energy

Total energy (E) is the sum of potential energy and kinetic energy, i.e., E = K + U
 
⇒ 102290.png also 102303.png
 
Hence, 102309.png
102315.png
102321.png
 
where 102327.png = Rydberg’s constant = 1.09 × 107 per m.

Ionization energy and potential

The energy required to ionize an atom is called ionization energy. It is the energy required to make the electron jump from the present orbit to the infinite orbit.
 
Hence
 
102333.png
 
For H2-atom in the ground state
 
102342.png
 
The potential through which an electron need to be accelerated so that it acquires energy equal to the ionization energy is called ionization potential.
 
102348.png

Excitation energy and potential

When energy is given to an electron from external source, it jumps to higher energy level. This phenomenon is called excitation.
 
The minimum energy required to excite an atom is called excitation energy of the particular excited state and corresponding potential is called exciting potential.
 
102354.png
and 102360.png

Binding energy (BE)

Binding energy of a system is defined as the energy released when it’s constituents are brought from infinity to form the system. It may also be defined as the energy needed to separate it’s constituents to large distances. If an electron and a proton are initially at rest and brought from large distances to form a hydrogen atom, 13.6 eV energy will be released. The binding energy of a hydrogen atom is therefore 13.6 eV.

Energy level diagram

The diagrammatic description of the energy of the electron in different orbits around the nucleus is called energy level diagram. The energy level diagram of hydrogen is given in Table 1.
 
Table 1: Energy level diagram of hydrogen/hydrogen like atom
 

Principle quantum number
Orbit
Excited state
Energy for H2 atom
102629.png
n
Infinite
Infinite
0 eV
102636.png
n = 4
Fourth
Third
–0.85 eV
102637.png
n = 3
Third
Second
–1.51 eV
102639.png
n = 2
Second
First
–3.4 eV
102641.png
n = 1
First
Ground
–13.6 eV




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