Concept:
Electron gain enthalpy is the enthalpy change when an isolated gaseous atom accepts an electron.
\[
X(g)+e^- \rightarrow X^-(g)
\]
More negative electron gain enthalpy means greater tendency to accept an electron.
Important periodic trends:
• Electron gain enthalpy generally becomes more negative across a period.
• It generally becomes less negative down a group.
• Oxygen has less negative value than sulphur because the small size of oxygen causes greater electron-electron repulsion.
• Chlorine has the most negative value among halogens, while bromine is more negative than iodine.
Step 1: Compare oxygen and sulphur.
Although oxygen lies above sulphur in Group 16, oxygen has a very small atomic size.
The incoming electron experiences strong repulsion in the compact \(2p\)-orbital.
Therefore,
\[
\Delta H_{eg}(O) > \Delta H_{eg}(S)
\]
or equivalently,
\[
O<S
\]
in terms of negativity.
Step 2: Compare bromine and iodine.
Bromine lies above iodine in Group 17.
Since bromine is smaller in size, it attracts the incoming electron more strongly.
Hence,
\[
Br>I
\]
with respect to electron affinity tendency.
Step 3: Arrange all elements.
Using known electron gain enthalpy values:
\[
O<S<I<Br
\]
This is the correct increasing order of negativity of electron gain enthalpy.
Step 4: Identify the correct option.
Therefore,
\[
\boxed{O<S<I<Br}
\]
Hence the correct option is
\[
\boxed{\text{(B)}}
\]