Calculate the volume occupied by the gas.

Step 1: Use Boyle's law for a gas at constant temperature, where pressure times volume is constant.

$P_1 V_1 = P_2 V_2$

Given:
$P_1 = 1~atm, \quad V_1 = 1~L, \quad P_2 = 4~atm$

Step 2: Rearrange to solve for the final volume $V_2$.

$V_2 = \frac{P_1 V_1}{P_2}$

Step 3: Substitute the values.

$V_2 = \frac{(1~atm)(1~L)}{4~atm}$

Step 4: Simplify.

$V_2 = \frac{1~L}{4} = 0.25~L$

Final answer: 0.25 L