The expression given is P=P0‌exp(−αt2), where P is a physical quantity, α is a constant, and t is time. Since the argument of the exponential function must be dimensionless (as the exponential function can only operate on dimensionless quantities), the term −αt2 must be dimensionless. This means that α must be chosen such that when it is multiplied by t2 (where t has dimensions of time, ([T]) , the result is a dimensionless quantity. Let's consider the dimensions of each component: The dimensions of P The dimensions of P and P0 are the same, as they are both representations of the physical quantity P. The dimension of time, t, is [T]. The exponential function does not add or change dimensions; it requires its argument to be dimensionless. To ensure the argument of the exponential −αt2 is dimensionless, α must have dimensions that cancel out the dimensions of t2. Since the dimensions of t2 are [T2],α must have dimensions that, when multiplied by [T]2, result in a dimensionless quantity. Therefore, α must have the dimensions of [T]−2. So, the correct option is: Option D: Have dimensions of t−2