Discussion
The dimensional formula for the product of the decay constant λ and the mean life τ of a radioactive substance is
Answer: D
The product \(\lambda\tau\) is dimensionless: \(L^{\circ}M^{\circ}T^{\circ}\) (all powers zero).
The decay constant has dimensions of inverse time, \([T^{-1}]\), and the mean life is a time, \([T]\). In fact \(\tau = 1/\lambda\), so
\[ [\lambda\tau] = [T^{-1}][T] = [L^{0}M^{0}T^{0}] \]
The product is the pure number 1. Every other option contains a non-zero power of L, M or T, which a dimensionless quantity cannot have.
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