Question

Element X is a radioactive isotope such that every 24 years, its mass decreases by

Answer 1

Answer:

Step-by-step explanation:

We get to use the simple version of the half life equation:

$N=N_0(\frac{1}{2})^{\frac{t}{H}$ where N is the amount of radioactive element left after a specific number of years,

N0 is the initial amount of the element,

t is the number of years (our unknown), and

H is the Half life of the element. For us,

N is 61

N0 is 70,

t is unknown,

H is 24 years. Filling in:

$61=70(.5)^{\frac{t}{24}$. We begin by dividing both sides by 70 to get:

$.8714285=(.5)^{\frac{t}{24}$ and then take the natural log of both sides:

$ln(.8714285=ln(.5)^{\frac{t}{24}$ which allows us to bring down the exponent to the front on the right side:

$ln(.8714285)=\frac{t}{24}ln(.5)$. We divide both sides by ln(.5) to get:

$.1985457976=\frac{t}{24}$ and then multiply both sides by 24 to get:

t = 4.8 years