Understand the assertion

Assertion $A$: The first ionisation enthalpy decreases across a period.

Across a period (from left to right), the general trend is that first ionisation enthalpy increases, not decreases.

This is because:

• nuclear charge increases,
• electrons are added to the same shell,
• shielding does not increase significantly,
• hence effective nuclear charge increases,
• electrons are held more strongly.

Therefore, Assertion $A$ is false.

Understand the reason

Reason $R$: The increasing nuclear charge outweighs the shielding across the period.

This statement is true.

Across a period:

• the number of protons increases,
• added electrons enter the same principal shell,
• shielding effect increases only slightly,
• so the net attraction on valence electrons increases.

Hence, the increasing nuclear charge indeed outweighs shielding.

Match with options

• Assertion $A$ = False
• Reason $R$ = True

Therefore, the correct option is:

$\boxed{\text{A: } A \text{ is false but } R \text{ is true}}$

Comparison with stored correct answer

Stored correct answer = $A$

Our derived answer also = $A$.

So they agree.