Which of the following statements regarding the energy of the stationary state is true in the following one-electron systems? [2026]

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Q.
Which of the following statements regarding the energy of the stationary state is true in the following one-electron systems [2026]

1 $- 1.09 \times 10^{- 18} J$ for second orbit of H atom.

2 $- 2.18 \times 10^{- 18} J$ for third orbit of ${Li}^{2 +}$ ion.

3 $+ 8.72 \times 10^{- 18} J$ for first orbit of ${He}^{+}$ ion.

4 $+ 2.18 \times 10^{- 18} J$ for second orbit of ${He}^{+}$ ion.

Ans.
(2)

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

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

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

Solution

Q.
Which of the following statements regarding the energy of the stationary state is true in the following one-electron systems [2026]

1 $- 1.09 \times 10^{- 18} J$ for second orbit of H atom.

2 $- 2.18 \times 10^{- 18} J$ for third orbit of ${Li}^{2 +}$ ion.

3 $+ 8.72 \times 10^{- 18} J$ for first orbit of ${He}^{+}$ ion.

4 $+ 2.18 \times 10^{- 18} J$ for second orbit of ${He}^{+}$ ion.

Ans.
(2)

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

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

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

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Solution

Q. Which of the following statements regarding the energy of the stationary state is true in the following one-electron systems [2026]

1 -1.09×10-18 J for second orbit of H atom.

2 -2.18×10-18 J for third orbit of Li2+ ion.

3 +8.72×10-18 J for first orbit of He+ ion.

4 +2.18×10-18 J for second orbit of He+ ion.

Ans. (2) En=-2.18×10-18 Z2n2 J/atom For 3rd orbit of Li2+ ion =-2.18×10-18×3232=-2.18×10-18 J.

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Q.
Which of the following statements regarding the energy of the stationary state is true in the following one-electron systems [2026]

1 $- 1.09 \times 10^{- 18} J$ for second orbit of H atom.

2 $- 2.18 \times 10^{- 18} J$ for third orbit of ${Li}^{2 +}$ ion.

3 $+ 8.72 \times 10^{- 18} J$ for first orbit of ${He}^{+}$ ion.

4 $+ 2.18 \times 10^{- 18} J$ for second orbit of ${He}^{+}$ ion.

Ans.
(2)

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

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

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