Question

The dimension of \( \lambda \times t \) (decay constant \(\lambda\) multiplied by time \(t\)) is:

• A. \( [T] \)
• B. \( [M^{-1}T^{-1}] \)
• C. \( [T^2] \)
• D. \( [1] \)

Hint:

For dimensional analysis, keep in mind that units can cancel out in products and quotients, and sometimes a quantity might end up dimensionless.

Answer 1

The Correct Option is A

The decay constant \( \lambda \) has the dimension of inverse time, i.e., \( [T^{-1}] \). Time \( t \) has the dimension of \( [T] \). So, the product \( \lambda \times t \) will have the dimension of: \[ [T^{-1}] \times [T] = [1] \] Thus, the dimension of \( \lambda \times t \) is dimensionless, and the correct answer is \( [1] \). But as given in the options, if it was \( [T^2] \), one might assume unit time measurement instead.