Question

Precalc question!!!!!!

Answer 1

The final mass of the radioactive substance is equal to 1.873 gram.

How to determine the final mass of an radioactive substance

In this problem we need to determine the mass after being desintegrated according to following formula:

`Q(t) = Q \cdot e^{-(t)/(\tau) }`

Where:

• Q - Initial mass, in grams.
• t - Time, in years.
• τ - Time constant, in years.

Where time constant is determined by:

`\tau = \frac{t_{(1)/(2)}}{\ln 2}`

Where
`t_{(1)/(2)}` is half-life, in years.

First, determine time constant:

`\tau = (8.93)/(\ln 2)`

`\tau = 12.883\,yr`

Second, determine the final mass of the radioactive substance: (Q = 6 g, τ = 12.883 yr, t = 15 yr)

`Q(15) = 6 \cdot e^{-(15)/(12.883) }`

Q(15) = 1.873 g

The radioactive substance has a final mass of 1.873 gram.