Two radioactive isotopes and start with equal numbers of nuclei

PHYSICS · Single correct · A Level · Physics · Nuclear physics · Nuclear physics

Problem

Two radioactive isotopes

X

and

Y

start with equal numbers of nuclei. After

20\,\text{days}

, isotope

X

has

25\%

of its original nuclei remaining, whereas isotope

Y

has

6.25\%

remaining. Both decay exponentially. Which statement best compares their half-lives? (a) Isotope

X

has half the half-life of isotope

Y

. (b) Isotope

X

has one and a half times the half-life of isotope

Y

. (c) Isotope

X

has twice the half-life of isotope

Y

. (d) Isotope

X

has four times the half-life of isotope

Y