A straight line representing a radioactive decay study passes through the points and…

CHEMISTRY · Subjective · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear

Problem

A straight line representing a radioactive decay study passes through the points

(t_{1}=4.0\,\text{min},\;\ln N_{1}=10.2)

and

(t_{2}=16.0\,\text{min},\;\ln N_{2}=7.8)

on a graph whose horizontal axis is time in minutes and vertical axis is

\ln N

. (a) Determine the numerical value of the slope of this line. (b) Hence find the decay constant

\lambda

\text{min}^{-1}

. (c) Calculate the mean life of the nuclei. (d) How long (from

t=0

) will it take for the activity of the sample to drop to

\dfrac{1}{20}

of its initial value?