Question

Calculate the energy associated with second orbit of \(\mathrm{He}^{+}\).

• A. \(-2.18\times 10^{-18}\text{ }\mathrm{J}\)
• B. \(-4.36\times 10^{-18}\text{ }\mathrm{J}\)
• C. \(-6.54\times 10^{-18}\text{ }\mathrm{J}\)
• D. \(-8.72\times 10^{-18}\text{ }\mathrm{J}\)

Hint:

Use the Bohr energy expression for a hydrogen-like ion with atomic number 2 and n equal to 2.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
For hydrogen-like species, \(E_n = -2.18\times 10^{-18}\dfrac{Z^2}{n^2}\text{ J}\).

Step 2: Calculation
For \(\text{He}^{+}\), \(Z = 2\) and \(n = 2\).
\(E_2 = -2.18\times 10^{-18}\times\dfrac{4}{4}\text{ J}\)
\(= -2.18\times 10^{-18}\text{ J}\).

Step 3: Compare the options
This matches the first option.

Final Answer:
The energy of the second orbit of He+ is \(-2.18\times 10^{-18}\) J. \[ \boxed{\text{(A) }-2.18\times 10^{-18}\text{ J}} \]