Two different radioactive isotopes, X and Y

PHYSICS · Subjective · A Level · Physics · Nuclear physics · Nuclear physics

Problem

Two different radioactive isotopes, X and Y, are investigated. When

\ln N

is plotted against time for each isotope, straight lines with slopes

m_{X}=-2.0\times10^{-3}\,\text{s}^{-1}

and

m_{Y}=-6.0\times10^{-3}\,\text{s}^{-1}

are obtained. (a) For each isotope, write the value of its decay constant. (b) Calculate the half-life of both isotopes. (c) Find the ratio

T_{1/2}^{(X)}:T_{1/2}^{(Y)}

and hence state which isotope is more stable.