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