A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons?

Solution

Physics sir · 3 steps

First find which level 10.2 eV lifts the electron to, then count the ways it can fall back.

1. Find the level. Hydrogen's levels are Eₙ = -13.6/n² eV. The jump from n = 1 to n = 2 needs E₂ - E₁ = -3.4 - (-13.6) = 10.2 eV, which matches the energy given exactly.
2. Count the lines. From level n, the number of possible spectral lines is n(n-1)/2. Here n = 2.

   N = n(n-1)/2 = (2 × 1)/2 = 1

3. So. The electron can only drop from n = 2 to n = 1. That gives one line, the first Lyman line at 10.2 eV, so the answer is (d) 1.

The idea to keep. Turn the energy into a quantum number first. Only then use n(n-1)/2, and remember that 10.2, 12.09 and 12.75 eV take hydrogen to n = 2, 3 and 4.

Answer from the NTA final answer key. Solution by PrepWiser.