Which of the following statements regarding the energy of the stationary state is true in the following one

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

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

A. +2.18 × 10⁻¹⁸ J for second orbit of He⁺ ion

B. +8.72 × 10⁻¹⁸ J for first orbit of He⁺ ion

C. −1.09 × 10⁻¹⁸ J for second orbit of H atom

D. −2.18 × 10⁻¹⁸ J for third orbit of Li²⁺ ion

Correct Answer: −2.18 × 10⁻¹⁸ J for third orbit of Li²⁺ ion

Explanation

For a one–electron system, the energy of the stationary state is given by:

$$ E_n = -2.18 \times 10^{-18} \frac{Z^2}{n^2}\ \text{J} $$

where Z is the atomic number and n is the principal quantum number.

For Li²⁺ ion, Z = 3 and for the third orbit, n = 3.

$$ E_3 = -2.18 \times 10^{-18} \times \frac{3^2}{3^2} $$

$$ E_3 = -2.18 \times 10^{-18}\ \text{J} $$

The negative sign indicates that the electron is in a bound state.

Hence, the correct statement is −2.18 × 10⁻¹⁸ J for third orbit of Li²⁺ ion.