Step 1: Understanding the energy gap in semiconductors.
In semiconductors, the forbidden energy gap is the energy difference between the valence band and the conduction band. For germanium, this gap is well known and can be calculated using the following relation for the energy gap \( E_g \) in terms of temperature and material properties.
Step 2: Use the known value for germanium.
The forbidden energy gap for germanium at room temperature is typically around \( 1.216 \times 10^{-19} \, \text{J} \), which corresponds to the value given in option (1).
Step 3: Conclusion.
The correct answer is \( 1.216 \times 10^{-19} \, \text{J} \), which is option (1).