Question

If the electron in a hydrogen atom moves from the ground state orbit to the $5^{\text{th}}$ orbit, then the potential energy of the electron

• A. is increased
• B. is zero
• C. is decreased
• D. remains unchanged

Hint:

Think of gravity as an analogy: pulling an object further away from its attractive center always increases its potential energy! Because the value moves from a deep negative well closer toward zero, it is mathematically increasing.

Answer 1

The Correct Option is A

Step 1: Recall the potential energy.
For the $n^{th}$ orbit, $U=\frac{-27.2}{n^2}$ eV, always negative.

Step 2: Compare the two orbits.
At $n=1$, $U=-27.2$ eV. At $n=5$, $U=\frac{-27.2}{25}\approx-1.09$ eV.

Step 3: Decide the trend.
$-1.09$ is greater (less negative) than $-27.2$, so the potential energy goes up as the electron moves outward. \[ \boxed{\text{is increased}} \]