Answer:
The wavelength of the energy that needs to be absorbed = 52.36 nm
Explanation:
For this study;
Let consider the Rydgberg equation from Bohr's theory of atomic model:
i.e.
[tex]\dfrac{1}{\lambda} = R_H (Z^*)^2( \dfrac{1}{n_1^2}-\dfrac{1}{n_2^2})[/tex]
where
Z* = effective nuclear charge of atom = Z - σ = 6
n₁ = lower orbit = 3
n₂ = higher orbit = 4
[tex]R_H[/tex] = Rydyberg constant = 1.09 × 10⁷ m⁻¹
λ = wave length of the light absorbed
∴
[tex]\dfrac{1}{\lambda} = 1.09 \times 10^7}(6)^2( \dfrac{1}{3^2}-\dfrac{1}{4^2})[/tex]
[tex]\dfrac{1}{\lambda} = 1.09 \times 10^7}(36)( \dfrac{1}{9}-\dfrac{1}{16})[/tex]
[tex]\dfrac{1}{\lambda} = 392400000\times0.0486111111[/tex]
[tex]\dfrac{1}{\lambda} =19075000[/tex]
[tex]\lambda = \dfrac{1}{19075000}[/tex]
[tex]\lambda = \dfrac{1}{1.91\times 10^7 \ m^{-1}}[/tex]
[tex]\lambda = 5.236 \times 10^{-8} m[/tex]
[tex]\lambda = 52.36 \times 10^{-9} m[/tex]
[tex]\lambda = 52.36\ n m[/tex]
Therefore, the wavelength of the energy that needs to be absorbed = 52.36 nm
