Step 1: Understand Electron Gain Enthalpy.
Electron Gain Enthalpy is the energy released when an electron is added to an isolated gaseous atom. More negative electron gain enthalpy indicates greater tendency to accept an electron.
Step 2: Identify the group of elements.
The elements \(Cl\), \(Br\), \(I\), and \(At\) belong to Group \(17\) (Halogens). Halogens generally have high electron gain enthalpy because they need one electron to complete their octet.
Step 3: Analyze the trend down the group.
As we move down the group, atomic size increases and shielding effect also increases. Due to this, the incoming electron experiences less attraction from the nucleus. Hence, the magnitude of electron gain enthalpy decreases down the group.
Step 4: Compare chlorine and bromine.
Chlorine has smaller atomic size than bromine, so it attracts the incoming electron more strongly. Therefore, chlorine has more negative electron gain enthalpy than bromine.
Step 5: Compare iodine and astatine.
Iodine has a smaller atomic size than astatine, so iodine has greater magnitude of electron gain enthalpy than astatine.
Step 6: Arrange in decreasing order.
Thus, the decreasing order of magnitude of electron gain enthalpy becomes
\[
Cl > Br > I > At
\]
Step 7: Final conclusion.
Hence, the correct decreasing order is
\[
\boxed{Cl > Br > I > At}
\]
Therefore, the correct answer is option (B).