Answer
The correct answer is:
(a) The spacings decrease.
Work Step by Step
We can write an expression for the energy level $E_n$:
$E_n = \frac{n^2~\pi^2~\hbar^2}{2~m~L^2}$, where $L$ is the length of the box.
If the box is made longer, then the value of $L$ increases. Then the energy levels will decrease thus making the spacings between energy levels smaller.
The correct answer is:
(a) The spacings decrease.
