Question

how chlorine is more reactive than iodine

Answer 1

Chlorine has a higher effective nuclear charge, and  should be more oxidizing than iodine.The nuclear charge of chlorine is less shielded by intervening electrons. So the chlorine gas will be a better oxidant.
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Answer 2

Chlorine has a higher effective nuclear charge, and therefore should be more oxidizing than iodine.

Explanation:

The nuclear charge of chlorine is less shielded by intervening electrons. Thus chlorine gas should be a better oxidant.

If we turn to reduction potentials, which we should do as scientists because scientists must utilize quantitative data, we find:

12Cl2+e−→Cl− E∘=1.36

12I2+e−→I− E∘=0.54