Rate of a reaction can be expressed by Arrhenius equation as: $$$k = Ae^{-E/RT}$$$ In this equation, E represents

The Arrhenius equation is written as $$k = A e^{-E/RT}$$ where:

• $$k$$ is the temperature-dependent rate constant.
• $$A$$ is the pre-exponential (frequency) factor that contains steric and collision-frequency terms.
• $$E$$ is the activation energy of the reaction (in $$\text{J mol}^{-1}$$).
• $$R$$ is the universal gas constant and $$T$$ is the absolute temperature.

By definition, the activation energy $$E$$ is the minimum energy that reacting molecules must possess for a successful (effective) collision leading to product formation. Hence:

• Molecules having energy $$\lt E$$ do not possess sufficient energy to cross the energy barrier, so they do not react.
• Molecules having energy $$\ge E$$ are able to overcome the barrier and can react if correctly oriented.

Therefore, $$E$$ represents the energy below which the colliding molecules will not react.

Checking each option:

Option A: “energy above which all the colliding molecules will react” — incorrect, because even with energy $$\gt E$$ molecules still need proper orientation; “all” is too strong.

Option B: “energy below which colliding molecules will not react” — correct; this matches the definition of activation energy.

Option C: “total energy of the reacting molecules at temperature $$T$$” — incorrect; total molecular energy is unrelated to $$E$$.

Option D: “fraction of molecules with energy greater than the activation energy” — incorrect; that fraction is given by $$e^{-E/RT}$$, not by $$E$$ itself.

Hence, the correct choice is Option B which is: the energy below which colliding molecules will not react.