For a radioactive isotope

CHEMISTRY · Single correct · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear

Problem

For a radioactive isotope, the number of undecayed nuclei after an elapsed time

t

is related to the initial number

N_0

N=N_0e^{-\lambda t}

, where

\lambda

is the decay constant. Which expression gives

t

in terms of

N_0

N

, and

\lambda

? (a)

\lambda\,\ln\!\left(\dfrac{N_0}{N}\right)

(b)

\dfrac{N_0-N}{\lambda}

(c)

\dfrac{1}{\lambda}\,\ln\!\left(\dfrac{N_0}{N}\right)

(d)

\dfrac{1}{\lambda}\,\ln\!\left(\dfrac{N}{N_0}\right)