Step 1: Recall the half-life idea.
The half-life is the time for half of a radioactive sample to decay. The decay constant $\lambda$ tells how fast the decay happens.
Step 2: Write the link between them.
The half-life and decay constant are tied by $T_{1/2} = \dfrac{0.693}{\lambda}$.
Step 3: Spot the relationship.
Since $\lambda$ is in the bottom of the fraction, the half-life is inversely proportional to $\lambda$. When one goes up, the other goes down.
Step 4: Apply the change.
The decay constant is doubled, so replace $\lambda$ with $2\lambda$: $T'_{1/2} = \dfrac{0.693}{2\lambda}$.
Step 5: Compare with the original.
This is exactly half of the original $T_{1/2} = \dfrac{0.693}{\lambda}$. So $T'_{1/2} = \dfrac{T_{1/2}}{2}$.
Step 6: State the result.
Doubling the decay constant makes the half-life become half of what it was. \[ \boxed{\text{Halves}} \]