Question

The energy associated with the first orbit of He+ is:

• A. 0J
• B. -8.72 × 10^-18 J
• C. -4.58 × 10^-18 J
• D. -0.545 × 10^-18 J

Hint:

Use the formula En​=−2.18×10−18×Z2/n2​ for hydrogen-like atoms.

Answer 1

The Correct Option is B

The energy of an electron in the \( n \)-th orbit of a hydrogen-like atom is given by the formula:

\( E_n = -2.18 \times 10^{-18} \times \frac{Z^2}{n^2} \)

For He⁺, \( Z = 2 \) (atomic number of helium) and \( n = 1 \) (first orbit):

\( E = -2.18 \times 10^{-18} \times \frac{2^2}{1^2} \)

\( E = -2.18 \times 10^{-18} \times 4 = -8.72 \times 10^{-18} \, \text{J} \)

Thus, the energy associated with the first orbit of He⁺ is \( -8.72 \times 10^{-18} \, \text{J} \).