Question

What is the energy of an electron in a hydrogen atom whose angular momentum is \(h/\pi\) ?

• A. \(-2.18\times 10^{-18}\) J
• B. \(-5.45\times 10^{-19}\) J
• C. \(-2.42\times 10^{-19}\) J
• D. \(-1.36\times 10^{-19}\) J

Hint:

Use mvr = nh/2pi to find n, then E_n = -2.18e-18/n^2 J.

Answer 1

The Correct Option is B

Step 1: Quantum number
Equating $\dfrac{nh}{2\pi}$ to $\dfrac{h}{\pi}$ gives $n=2$, the second orbit.

Step 2: Use energy in eV
$E_2=-\dfrac{13.6}{4}=-3.4$ eV.

Step 3: Convert to joules
$-3.4\times1.6\times10^{-19}\approx-5.45\times10^{-19}$ J, which is option (B).

Final Answer:
The energy is about $-5.45\times10^{-19}$ J. \[ \boxed{\text{(B) }-5.45\times10^{-19}\text{ J}} \]