Step 1: Start with the trigger.
Breathing fast and deep washes $CO_2$ out of the blood quicker than it is produced.
Step 2: Work out the acid base shift.
Since $CO_2$ forms carbonic acid in blood, losing $CO_2$ pushes blood pH up, giving respiratory alkalosis.
Step 3: Follow the calcium.
Blood calcium exists in two pools, one stuck to albumin and one free (ionised). A higher pH changes the charge on albumin so that it grabs more calcium than usual. Total calcium stays the same, but the ionised share drops.
Step 4: Explain the spasm.
Nerves and muscle fibres depend on ionised calcium to keep their membranes calm. With less of it around, the membrane threshold for firing drops, so nerves fire spontaneously and muscles go into spasm, a state called tetany.
Step 5: Eliminate the distractors.
The falling $CO_2$ is the starting trigger, not the direct cause of spasm. Potassium and sodium are not the ions responsible for this classic hyperventilation tetany.
Step 6: Final answer.
\[ \boxed{\text{Decreased ionised calcium}} \]