Two radioactive isotopes, X and Y

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

Two radioactive isotopes, X and Y, are available for use in an experiment. Their molar masses are

M_{\!X}

and

M_{\!Y}

, and their half-lives are

T_{\!X}

and

T_{\!Y}

, respectively. Equal masses

m

of each isotope are prepared. (a) Derive an expression for the ratio of their initial activities

A_{X}/A_{Y}

in terms of

m

M_{\!X}

M_{\!Y}

T_{\!X}

, and

T_{\!Y}

. (b) Using

m = 1.0\,\text{g}

M_{\!X}=60\,\text{g mol}^{-1}

T_{\!X}=4.0\,\text{h}

M_{\!Y}=30\,\text{g mol}^{-1}

, and

T_{\!Y}=8.0\,\text{h}

, compute the numerical value of

A_{X}/A_{Y}

. Comment on which isotope would produce the higher count rate at the start of the experiment.