Question

The time dependence of physical quantity P
is found to be of the form
P = P0e–αt2
Where‘t’ is the time and α is some constant.
Then the constant α will

Answer 1

Given:
The time dependence of physical quantity P is found to be of the form

p=poexp(-α t2)

αt2 is dimensionless

Therefore:
α=1/t2
=1/[T2]
=[T-2] or[T⁻²]

Conclusion :
constant α will [T-2] or[T⁻²]

Answer 2

Answer: dimensions of alpha = T^-2

Explanation:

Let alpha = a

Given: P =Po exp (-at^2)

Now for the given case to be true,

at^2 has to be dimensionless

i.e, at^2 = 1 (since all dimensionless quantities are always equated to unity)

By solving we get:. a = 1/t^2

= t^-2