Atomic StructureHard

Question

Which of the following statements regarding the energy of the stationary state is true in the following one-electron system ?

Options

A.$- 1.09 \times 10^{- 18}\text{ }J$ for second orbit of H atom.
B.$+ 2.18 \times 10^{- 18}\text{ }J$ for second orbit of ${He}^{+}$ion
C.$+ 8.72 \times 10^{- 18}\text{ }J$ for first orbit of ${He}^{+}$ion
D.$- 2.18 \times 10^{- 18}\text{ }J$ for third orbit of ${Li}^{2 +}$ ion

Solution

$E_{n} = - 2.18 \times 10^{- 18}\frac{Z^{2}}{n^{2}}\text{ }J/$ atom .

For $3\ ^{\text{rd~}}$ orbit of ${Li}^{+ 2}$ ion

$= - 2.18 \times 10^{- 18} \times \frac{3^{2}}{3^{2}} = - 2.18 \times 10^{- 18}\text{ }J$.

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