Question

The half-life of carbon-14 is 5730 years. Assume that the decay rate is proportional to the amount. Find the age of a sample in which 10% of C-14 originally present have decayed.
Select the correct answer.

a.

950 years

b.	1050 years

c.	1150 years

d.

850 years

e.

none

Answer 1

Solution: While dealing with half- life question, use half-life formula, that is given below:

  

Here,

y= Final amount

a= Initial amount

b=Growth/Decay

t= Time elapsed

h= Half-life

Start substituting known values in the above formula.

In this question , y= 100% - 10% =90% , since 10% of the sample decayed, leaving 90% to remain. So y is expressed as 90, derived from 90%, but without using "%".

Similarly, expressed a as 100, derived from 100%, but without using "%".

The value of b= 100% - decay rate, or in this case , b= 100% - 50% = 50%, or in fractional form , 1/2.

Divide both sides by 100, we get

Then we take logarithm on both sides of above equation , to make the bases same on both sides of the equation.

Now solved t , we get ,

t = 870.97 = 871 years old approximately.

Answer: The sample is approximately 871 years old. Hence, option (e) none is correct.