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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

CBSE Class 12 Physics Notes: Dual Nature of Radiation and Matter - Important Formulas

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 (DE) when an electron is excited from a lower state n1 to any higher state n2 is given as:

CBSE Class 12 Physics Notes: Dual Nature of Radiation and Matter - Important Formulas

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

CBSE Class 12 Physics Notes: Dual Nature of Radiation and Matter - Important Formulas

Illustration 1: A doubly ionised Lithium atom is hydrogen like with atomic number 3.

(i) Find the wavelength of radiation required to excite the electron in Li++ from the first to the third Bohr Orbit. (Ionization energy of the hydrogen atom equals 13.6 eV).

(ii) How many spectral lines are observed in the emission spectrum of the above excited system?

Solution:

CBSE Class 12 Physics Notes: Dual Nature of Radiation and Matter - Important Formulas

(ii) From the excited state (E3), coming back to ground state, there can be 3C2 = 3  possible radiations.

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