calculate the wavelength of the light emitted when an electron in a hydrogen atom n=3 to n=1

 TO CALCULATE THE

 to calculate the wavelength of the emit light when an electron  move from n=3 to n= 1,

 we start by                    

calculating the energy difference between these two levels

∆E = E₃ – E₁

E₃= E₀ /n²

but E₀  = -13.6 eV

 = -13.6/9

=-1.511

E₁ = E₀ /n²

 = -13.6/1

 =-13.6

 the energy difference is

∆E = E₃ – E₁

=-1.511-(-13.6)

= 12.0889 eV

from E = hf = hc/λ

λ =hc/E

all symbols have their usual meaning

λ = (6.626× 10^-34 × 3×10⁸)/ 12.0889 eV

but eV  =1.6×10-¹⁹c

therefore λ = (6.626× 10^-34 × 3×10⁸)/ 12.0889 ×1.6×10-¹⁹c