Answer:
λ₂ = 1,219 10⁻⁷ m , λ₃ = 1.028 10⁻⁷ m , λ₄ = 0.9741 10⁻⁷ m , λ₅ = 0.9510 10⁻⁷ m and λ₆ = 0.9395 10⁻⁷ m
Step-by-step explanation:
To calculate the lines of the hydrogen liman series, we can use the Bohr atom equation
En = -13.606 / n² [eV]
n En
1 -13,606
2 -13.606 / 4 = -3.4015
3 -13.606 / 9 = -1.5118
4 -13.606 / 16 = -0.8504
5 -13.606 / 25 = -0.5442
6 -13.606 / 36 = -0.3779
The lyma series are transitions where the state is fundamental (E1), let's calculate the first five transitions
State
initial final energy
6 1 -0.3779 - (- 13.606) = 13.23 eV
5 1 -0.5442 - (- 13.606) = 13.06 eV
4 1 -0.8504- (-13.606) = 12.76 eV
3 1 -1.5118 - (- 13.606) = 12.09 eV
2 1 -3.4015 - (- 13.606) = 10.20 eV
Let's use the relationship between the speed of light and the wavelength and the frequency
c = λ f
f = c / λ
Planck's relationship for energy
E = h f
E = h c / λ
λ = hc / E
We calculate for each energy
E = 10.20 eV
λ = 6.63 10⁻³⁴ 3 10⁸ / (10.20 1.6 10⁻¹⁹)
λ = 12.43 10⁻⁷ / 10.20
λ₂ = 1,219 10⁻⁷ m
E = 12.09 eV
λ₃ = 12.43 10⁻⁷ / 12.09
λ₃ = 1.028 10⁻⁷ m
E = 12.76 eV
λ₄ = 12.43 10⁻⁷ /12.76
λ₄ = 0.9741 10⁻⁷ m
E = 13.06 ev
λ₅= 12.43 10⁻⁷ /13.06
λ₅ = 0.9510 10⁻⁷ m
E = 13.23 eV
λ₆ = 12.43 10⁻⁷ / 13.23
λ₆ = 0.9395 10⁻⁷ m