Solve the problem.
-The half-life of an element is $5.1 \times 10 ^ { 8 } \mathrm { yr }$. How long does it take a sample of the element to decay to $\frac { 2 } { 5 }$ of its original mass? (Express results in scientific notation, rounded to the nearest hundredth.)
A) $5.80 \times 10 ^ { 8 } \mathrm { yr }$
B) $6.74 \times 10 ^ { 8 } \mathrm { yr }$
C) $1.14 \times 10 ^ { 8 } \mathrm { yr }$
D) $3.24 \times 10 ^ { 8 } \mathrm { yr }$

Question

Quizplus · Accepted Answer

The decay formula is $ N(t) = N_0 \times (1/2)^{t/T} $. Solving for $ t $ when $ N(t)/N_0 = 2/5 $ and $ T = 5.1 \times 10^8 $ gives $ t \approx 6.74 \times 10^8 $ years.

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