A student tries to test the radioactive decay law using dimensional analysis
PHYSICS · Single correct · CBSE · Physics · Units and Measurements · Units and Measurements
Problem
A student tries to test the radioactive decay law N=N0e−λt using dimensional analysis. Which of the following statements about this attempt is correct?
(a) λ and t must have the same dimensions; checking this alone completely verifies the decay law.
(b) The equation is dimensionally inconsistent because the exponent should possess the units of time.
(c) Dimensional analysis cannot confirm the decay law’s exponential form; the method fails whenever the relation involves an exponential of a dimensionless quantity.
(d) Any relation that contains an exponential term is automatically dimensionless and therefore always passes a dimensional check.