Question

What is the energy of an electron in a hydrogen atom in a stationary state corresponding to n = 2 ?

• A. \(-5.45\times 10^{-19}\) J
• B. \(-2.40\times 10^{-19}\) J
• C. \(-4.35\times 10^{-18}\) J
• D. \(-6.70\times 10^{-18}\) J

Hint:

Use E_n = -2.18e-18 J / n squared and put n = 2.

Answer 1

The Correct Option is A

Step 1: Use the Rydberg energy in eV:
The energy of level $n$ is $-13.6/n^2$ eV.

Step 2: Compute:
For $n=2$: $E_2 = -13.6/4 = -3.4$ eV.

Step 3: Convert to joules:
$1\ \text{eV} = 1.602\times10^{-19}$ J, so $E_2 = -3.4 \times 1.602\times10^{-19} = -5.45\times10^{-19}$ J.
The other values do not come from any whole number $n$, so option (A) alone fits.

Final Answer:
The energy is -5.45e-19 J. \[ \boxed{\text{(A) }-5.45\times 10^{-19}\ \text{J}} \]