Question

Suppose a future astronaut travels to a distance planet around a distant star. They collect rocks for dating the age of the planet and system. The astronaut compares the abundance of a certain radioactive element (half life of element = 500 million years) in the collected rocks to the abundance of the same element in a newly formed rock. They measure that there are 1/16th the number of radioactive atoms in the collected sample. How old is this planet?

a. 8 billion years old.
b. 4 billion years old.
c. 1 billion years old.
d. 2 billion years old.
e. 16 billion years old.

Answer 1

The correct option is d

d. 2 billion years old.

Step-by-step explanation:

The general formula to for the half life on an element is given as:

`N(t)=N_o~ ((1)/(2))^{(t)/(t(1/2))}`

Where

N(t) = Quantity of the substance remaining.

N(o) = Quantity of the substance which was initially present

t = time elapsed

t(1/2) = half life of the substance

In this question, we have to find t using the above formula, where

N(t) = 1/16

N(o) = 1

t(1/2) = 500

Substitute in the given formula:

`1=(1)/(16)~ ((1)/(2))^{(t)/(500)}\\\text{Solve the equation for t}\\t = 2000`

Hence, the time planet has been into existence, or how old the planet is:

t = 2000 million years

or

t = 2 billion years