Question

Determine the wavelength of the energy that needs to be absorbed for a 3p electron in chlorine to be promoted to the 4s subshell. Assume that Zeff=6 for a chlorine atom.

Answer 1

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.

$\dfrac{1}{\lambda} = R_H (Z^*)^2( \dfrac{1}{n_1^2}-\dfrac{1}{n_2^2})$

where

Z* = effective nuclear charge of atom = Z - σ = 6

n₁ = lower orbit = 3

n₂ = higher orbit = 4

$R_H$ = Rydyberg constant = 1.09 × 10⁷ m⁻¹

λ = wave length of the light absorbed

∴

$\dfrac{1}{\lambda} = 1.09 \times 10^7}(6)^2( \dfrac{1}{3^2}-\dfrac{1}{4^2})$

$\dfrac{1}{\lambda} = 1.09 \times 10^7}(36)( \dfrac{1}{9}-\dfrac{1}{16})$

$\dfrac{1}{\lambda} = 392400000\times0.0486111111$

$\dfrac{1}{\lambda} =19075000$

$\lambda = \dfrac{1}{19075000}$

$\lambda = \dfrac{1}{1.91\times 10^7 \ m^{-1}}$

$\lambda = 5.236 \times 10^{-8} m$

$\lambda = 52.36 \times 10^{-9} m$

$\lambda = 52.36\ n m$

Therefore, the wavelength of the energy that needs to be absorbed  = 52.36 nm