Question

Say, you observe a heated gaseous sample of $L{i}^{++}$ atoms, knowing that all the electrons are in the third Bohr orbits. How many spectral lines will you find in the emission spectrum of this sample?

• A. Infinitely many - it will be a continuous spectrum
• B. 3
• C. 5
• D. 1

Answer 1

The correct option is B 3

Each electronic transition from a higher Bohr orbit to a lower one will emit discrete radiation of particular frequency ν given by Bohr's energy postulate $E_i-E_f=hv.$ We know that the electrons in all the atoms of $L{i}^{++}$ sample are in orbits n=3. In how many ways can the atoms reach a more stable state (a lower energy level)?

1. Some of the electrons will fall from n = 3 to n = 2, emitting a particular frequency of light.
2. These electrons which just fell from to n = 3 to n = 2, will further jump from n = 2 to the ground state orbit , thus emitting a different frequency of light.
3. Some of the electrons which were in n = 3 initially will directly jump down to the ground state orbit n = 1, emitting a third frequency of light.

There will be three lines in the emission spectrum for this sample!

A general observation to make here is that here 3 states are possible for electron to have. n=3,2&1.
Its just a problem of permutation and combination now. The number of ways to select 2 lines out of the given 3 lines will be the number of transitions that the electron can make from 3 to reach 1.
So $3C_2$ = 3