Question

A doubly ionized lithium atom can be considered as a hydrogen like atom with atomic number 3. An electron is to be excited from the first to third Bohr’* orbit (ionizon energy of hydrogen atom is 13.6 eV). The wavelength of the radiation required to achieve this excitation is

(1) 0.114×10–6 m

(2) 114.26 A

(3) 0.114 A

(4) 1142 A

Answer 1

Correct option : (2) 114.26 A

Explanation :

Th energy of the electron in nth Bohr’* orbit with atomic number z is given by z2 (En of hydrogen)

Energy E1 for lithium++ in Ist Bohr orbit is – (13.6) × 9 eV

Energy E3 for lithium++ in 3rd Bohr orbit is

∴ Energy required for excitation from n = 1 to n = 3 for lithium++

E3 – E1 = 13.6(9 – 1) = 13.6 × 8 eV = 13.6 × 8 × 1.6 × 10–19 J

The wavelength λ of radiation required for this excitation to happen is