The Atom $40 \mathrm {~K}$ Decays Radioactively to the Gas $40 \mathrm { Ar }$

Multiple Choice

The atom $40 \mathrm {~K}$ decays radioactively to the gas $40 \mathrm { Ar }$ . An ancient rock is found to contain enough $40 \mathrm { Ar }$ gas to indicate that $77.0 \%$ of the $40 \mathrm {~K}$ in the rock has decayed to $40 \mathrm { Ar }$ ince the rock solidified. (Any previous argon would have boiled out of liquid rock.) How long ago did the rock solidify? The half-life of $40 \mathrm {~K}$ is $1.25$ billion years.

A) $0.471$ billion years
B) $2.65$ billion years
C) $0.324$ billion years
D) $1.80$ billion years