Question

Calculate the energy associated with third orbit of $\text{He}^+$.

• A. $-4.8 \times 10^{-19} \text{ J}$
• B. $-1.45 \times 10^{-19} \text{ J}$
• C. $-19.36 \times 10^{-19} \text{ J}$
• D. $-9.69 \times 10^{-19} \text{ J}$

Hint:

Don't forget $Z^2$ in the numerator for Helium! $Z=2$, so you must multiply by 4.

Answer 1

The Correct Option is D

Step 1: Concept
The energy of an electron in the $n$th orbit of a hydrogen-like species is $E_n = -2.18 \times 10^{-18} \times (Z^2 / n^2) \text{ J}$.

Step 2: Meaning
For $\text{He}^+$, the atomic number $Z = 2$. The third orbit means $n = 3$.

Step 3: Analysis
$E_3 = -2.18 \times 10^{-18} \times (2^2 / 3^2)$ $E_3 = -2.18 \times 10^{-18} \times (4 / 9)$ $E_3 = -2.18 \times 10^{-18} \times 0.444$ $E_3 \approx -0.9688 \times 10^{-18} = -9.69 \times 10^{-19} \text{ J}$

Step 4: Conclusion
The energy associated with the third orbit is $-9.69 \times 10^{-19} \text{ J}$. Final Answer: (D)