Ionisation energy is the energy required to remove the electron from respective orbit to n = ∞ i.e. Energy required to send the electron from respective orbit n to n = ∞
Given that the energy required to remove the electron from n = 1 to n = ∞ is -313.8 kcal/mole.
we know the relation E = hc/λ
⇒ Energy required to remove the electron is inversely proportional to wavelength.
⇒ Energy required to remove the electron is Directly proportional to wavenumber.
we know that wavenumber is given by R × (1/n₁² - 1/n₂²)
given ionisation energy is when n = 1 and n = ∞
then wavenumber corresponding to this R × (1 - 0) = R
we know that in the second excited state the electron is in the orbit - n =3
and ionisation energy is the energy required to send the electron from n = 3 to n = ∞
wavenumber corresponding to this is R ×(1/3² - 1/∞²) = R/9
the wavenumber corresponding to n = 3 to n = ∞ is one ninth the wavenumber corresponding to n = 1 to n = ∞
as the energy is directly proportional to wavenumber, the energy required to send away the electron from n = 3 to n = ∞ is one ninth the energy required to send away the electron from n = 1 to n = ∞
Given that the energy required to remove the electron from n = 1 to n = ∞ is -313.8 kcal/mole.
⇒ Energy required to send away the electron from n = 3 to n = ∞ is 1/9 × -313.8
⇒ Energy required to send away the electron from n = 3 to n = ∞ is -34.87 kcal/mole.
Ionisation energy of the electron in 2nd excited state is -34.87 kcal/mole.
