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

An electron jumps from orbit of higher energy to an orbit of lower energy which radiates energy in form of photons. The energy emitted is equal to difference in the energies from the two orbits.

The equation or formula for Bohr model for third postulate is given as,

hv = E_n – E_p

ΔE= E_n – E_p

ΔE = difference in energies of higher orbit and lower orbit.

E_n = energies of nth higher orbit and E_p =energies of p^th lower orbit

h = Planck’s constant

v = frequency of radiation emitted or absorbed

Electron of an atom orbiting around a nucleus are permitted to revolve in those orbit for which angular momentum is equal to integral multiple of h/2π, where h is the Planck’s constant.

The equation or formula for Bohr model for postulate 2 is given as,

m v_n r_n = n h / 2π

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

v_n = velocity of electron in nth state (orbit)

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

r_n = radius of nth orbit

n is a positive integer