Physics

Problem

A nuclide

X

decays into

Y

with decay constant

\lambda_X

. Nuclide

Y

subsequently decays into a stable product with decay constant

\lambda_Y

. If

\lambda_X\ll \lambda_Y

, which statement best describes how the activity of

Y

changes with time? a) The activity of

Y

rises to a maximum and then decays at approximately the fast rate

\lambda_Y

, largely independent of nuclide

X

. b) The activity of

Y

quickly reaches a constant value equal to

(\lambda_X/\lambda_Y)

times the activity of

X

and then remains steady. c) The activity of

Y

rises to a maximum and then decays at approximately the same slow rate as nuclide

X

. d) Because

\lambda_X

is so small, the production of

Y

is negligible, so its activity stays near zero at all times.