First slide

Classical atomic models

Question

$Given, ΔE = {\bar{R}}_{H} Z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$
$R_{H}$ (Rydberg constant) for H-atom is x m^-1. Corresponding value for this constant for He⁺ ion is

Moderate

A

100x cm^-1
B

400x cm^-1
C

4x cm^-1
D

0.04x cm^-1

Solution

$\begin{array}{l} \bar{v} = {\bar{R}}_{H} Z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] \\ {\bar{R}}_{H} = \frac{2 π^{2} {me}^{4} k^{2}}{{ch}^{3}} \\ = x m^{- 1} for H - atom \\ {\bar{R}}_{Z} = \frac{2 π^{2} {me}^{4} k^{2}}{{ch}^{3}} (Z^{2}) \end{array}$
For a species of atomic number Z (with one electron only)
$\begin{array}{l} \frac{{\bar{R}}_{Z}}{{\bar{R}}_{H}} = Z^{2} \\ ∴ {\bar{R}}_{Z} = (2)^{2} {\bar{R}}_{H} = 4 \times m^{- 1} = \frac{4 \times}{100} ({cm}^{- 1}) = 0 .04 \times {cm}^{- 1} \end{array}$

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