Concept: According to Bohr's postulates and the principle of conservation of energy, the energy of an emitted photon exactly equals the energy difference between the initial and final energy states of the atom.

Formula:
$$ \Delta E = E_2 - E_1 $$
$$ E_{\text{photon}} = \frac{hc}{\lambda} $$

Solution:

• Set the transition energy equal to the photon energy: \( E_2 - E_1 = \frac{hc}{\lambda} \).
• To isolate wavelength (\( \lambda \)), multiply both sides by \( \lambda \) and divide by the energy difference \( (E_2 - E_1) \).
• This algebraically yields: \( \lambda = \frac{hc}{E_2 - E_1} \).

Why other options are incorrect:
Option A is the wave number (inverse wavelength \( 1/\lambda \)). Option C subtracts the higher energy from the lower energy, incorrectly producing a negative wavelength. Option D incorrectly arranges the fundamental constants \( h \) and \( c \).