Question

An electron in a hydrogen atom drops from energy level e3 to e2. what's the frequency of the emitted photon

Answer 1

For this problem we can use 2 equations.
(1) - E = mC²
          E = Energy of photon (J)
          m = Mass of photon (kg) (1.67x10⁻²⁷ kg)
          C = speed of light (3 x 10⁸ m/s)

(2) - E = hf
        E = Energy of photon (J)
        h = plank's constant (6.63 × 10⁻³⁴J s)
        f  = frequency of the photon (Hz)

(1) = (2)
hence, mC² = fh                
                
by rearranging, 
                f =  mC² / h 
                f  =  1.67x10⁻²⁷ kg * (3 x 10⁸ m/s)² / (6.63 × 10⁻³⁴J s)
              f    = 2.27 x 10²³ Hz