calculate the wavelength of the light emitted when an electron in a hydrogen atom n=5 to n=4

to calculate the wavelength of the emit light when an electron  move from n=5 to n= 4,

 we start by

calculating the energy difference between these two levels

∆E = E₅ – E₄

E₅= E₀ /n²

but E₀  = -13.6 eV

 = -13.6/25

=-0.4857 eV

E₄ = E₀ /n²

 but E₀  = -13.6 eV

 = -13.6/16

=-0.85 eV

the energy difference is

∆E = E₅ – E₄

=-0.4857-(-0.85)

= 0.3645

from E = hf = hc/λ

λ =hc/E

all symbols have their usual meaning

λ = (6.626× 10^-34 × 3×10⁸)/ = 0.3645 eV

but eV  =1.6×10-¹⁹c

therefore λ = (6.626× 10^-34 × 3×10⁸)/ (= 0.3645

×1.6×10-¹⁹)

 use your calculator