The kinetic energy of an object is the energy that it attains due to its motion. It is the work needed to accelerate a body of a given mass from rest to its stated velocity.

The formula for Kinetic energy of an electron in nth orbit is given as,

K.E. = m e⁴ / 8 ε₀² n² h²

m= mass of an electron

e = Charge on an electron (1.6 x 10–19 C)

ε₀ = permittivity of free space

n = positive integer

h = Planck’s constant

The kinetic energy of an object is the energy that it attains due to its motion. It is the work needed to accelerate a body of a given mass from rest to its stated velocity.

The formula for Kinetic energy of an electron is given as,

K.E. = e² / 8π ε₀ r

ε₀ = permittivity of free space

e = Charge on an electron (1.6 x 10–19 C)

r = radius of the orbit of an electron

The electron in an atom is restricted to revolve in certain allowed circular orbit known as stationary orbit. The centripetal force for its motion is provided by electrostatic force of attraction between positively charged nucleus and negatively charged electron.

The formula for velocity of an electron in the nth orbit is given as,

v_n = 2π² Kme² Z / nh

v_n =velocity

K = 1/(4πε₀) = constant = 9 x 10⁹ N m² C^–2    

m= mass of an electron (9.1 x 10–31 Kg)

 e = Charge on an electron (1.6 x 10–19 C)

Z= atomic number (No. of Protons)

h= Planck’s constant (6.67 x 10^–34 J-s)

n is a positive integer.

The electron in an atom is restricted to revolve in certain allowed circular orbit known as stationary orbit. The centripetal force for its motion is provided by electrostatic force of attraction between positively charged nucleus and negatively charged electron.

The formula for radius r in the nth orbit of an electron

 r_n = n²h² / 4π² Kme² Z

r_n = radius of nth orbit

h= Planck’s constant (6.67 x 10^–34 J-s)

n is a positive integer

m= mass of an electron (9.1 x 10–31 Kg)

Z= atomic number (No. of Protons)

K = 1/(4πε₀) = constant = 9 x 10⁹ N m² C^–2     

e = Charge on an electron (1.6 x 10–19 C)

The energy of a photon emitted or absorbed is given by using Planck’s relation. It states that the energy of a photon, E, is proportional to its frequency, ν.

The formula for Planck’s relation between energy and frequency of radiation emitted or absorbed is given as,

E ∝ v

E = hv

E = Energy

h = Planck’s constant

v = frequency of radiation emitted or absorbed