Short Review of formulas (for one electron atom or ions):

1.     Velocity of electron in nth orbit = vn = 2.165 x 106 Z/n m/s

2.     Radius of nth orbit = rn = 0.53 x 10–10 n2/Z m

3.     Binding energy of an electron in nth state = En = –13.6 Z2/n2 eV/atom

       En = –2.17 × 10–16 Zn2/n2 J/atom = –13.6 Zn2/n2 eV/atom

4.     Kinetic energy = KE = 1/2 mv2n = KZe2 / rn 

5.     Potential energy = PE = –kZe2 / 2rn 

6.     Total energy of an electron = –En = –kZe2 / 2rn

        PE = 2TE ; PE = –2KE ; TE = –KE

7.     Binding energy of an electron in nth state

        En = –13.6 / n2 Z2 eV 

8.     Ionisation Energy = – B.E.

        I.E. = + 13.6 / n2 Z2 eV

9.     Ionisation Potential

        Ionisation potential = I.E. / e = 13.6/n2 Z2 

10.    Excitation Energy

The energy taken up by an electron to move from lower energy level to higher energy level. Generally it defined from ground state.

         Ist excitation energy = transition from n1 = 1 to n2 = 2

         IInd excitation energy = transition from n1 = 1 to n2 = 3

         IIIrd excitation energy = transition from n1 = 1 to n2 = 4 and so on …

         The energy level n = 2 is also called as Ist excited state.

         The energy level n = 3 is also called as IInd excited state. & so on …

In general, excitation energy (ΔE) when an electron is excited from a lower state n1 to any higher state n2 is given as:

            ΔE = 13.6 Z2 (1/n12 – 1/n22) eV 

11.    Energy released when an electron jumps from a higher energy level (n2) to a lower energy level (n1) is given as:

            ΔE = 13.6 Z2 (1/n12 – 1/n22) eV

If v be the frequency of photon emitted and λ be the wavelength, then:

            ΔE =hv = h c/λ

The wavelength (λ) of the light emitted an also be determined by using:

            1/λ = v = R Z2 (1/n12 – 1/n22)

            R = 1.096 x 107 /m

Important: Also remember the value of 1/R = 911.5 Å for calculation of λ to be used in objectives only).

12.    The number of spectral lines when an electron falls from n2 to n1 = 1 (i.e. to the ground state) is given by:

No. of lines = n2(n2–1) / 2

If the electron falls from n2 to n1, then the number of spectral lines is given by:

No. of lines = (n2  n1 + 1) (n2–n1) / 2

Related Resources
Energy Levels of Hydrogen Atom

Energy Levels of Hydrogen Atom The spectrum of...

Nucleus

The Nucleus The nucleus is the fundamental unit of...

Solved Examples of Structure of Atom

Solved Examples on Structure of Atom Atoms are the...

Nuclear Forces

Nuclear Forces The protons and neutrons are held...

Mass Defect and Binding Energy

Mass Defect Binding Energy The nucleons are bound...

Bohr Model

Bohr Model Bohr Model was introduced after the...