Ahydrogen atom in the ground state absorbs a photon that increases its principle quantum number by 3. how many different wavelengths could the atom emit on the decay path back to the ground state? (ignore spin-orbit coupling for this question).

so these are

either 3 to 2 or 2 to 1 or 3 to 1

Explanation:

As we know that total number photons emitted from nth state to ground state is given by

here it shows that if electron has transition from nth excited state to ground state then total number of photons is given by above equation

here we know that higher state is n = 3

so total number of photons is given as

so these are

either 3 to 2 or 2 to 1 or 3 to 1