Answer:
a) λ = 121.5 nm , b) 102.6, 97, 91.1 nm
Explanation:
Bohr's model describes the energy of the hydrogen atom
= k² e² / 2m (1 / n²)
A transition occurs when the electron passes from n level to a lower one
-
= k² e² / 2m (1 /
² - 1 /
²)
Planck's relationship is
E = h f = h c / lam
hc /λ = k² e²/ 2m(1 / ² - 1 /
²)
1 / λ = [k² e² / 2m h c] (1 / ² - 1 /
²)
1 /λ = Ry] (1 / ² - 1 /
²)
a) the first element of the series occurs for = 2
1 / λ = 1.097 10⁷ (1- 1/2²)
1 / λ = 1.097 10⁷ (1- 0.25)
1 / λ = 0.82275 10⁷
λ = 1.215 10⁻⁷ m
λ = 1,215 10⁻⁷ m (10⁹nm / m)
λ = 121.5 nm
b) the next elements of the series occur to
1 /λ λ (10-7m) λ (nm)
3 1 1,097 10⁷ (1-1 / 9) 1,0255 102.6
4 1 1,097 10⁷ (1-1 / 16) 0.9723 97.2
∞ 1 1,097 10⁷ (1 - 0) 0.91158 91.1