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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 V 

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


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