Question

Ytterbium decays 50% every 4.2 days. How much of an 80g sample would be left after 54.6 days? Use exponential decay formula.

A. 67 g
B. 53,211.33 g
C.41.76 g
D. 9.80 g
E. 0.12 g

Answer 1

Answer: Option E

`0.120\ g`

Explanation:

The exponential decay formula is:

`C (t) = pe^ {-rt}`

Where p is the initial amount of Ytterbium

r is the rate of decrease

C(t) is the amount of Ytterbium in grams as a function of time

t is the time in days

In this problem:

`p = 80\ g\\\\r=(50\%)/(100\%)\\\\r=0.5`

t is the time in units of 4.2 days

Then

`C(t) = 80e^(-0.5t)`

We want to calculate the amount of Ytterbium in 54.6 days.

Then as t is the time in units of 4.2 days

`t = (54.6)/(4.2) = 13\\\\t = 13`

Finally

`C(t=13) = 80e^(-0.5*13)`

`C(t) = 0.120\ g`