Question

What is the age of a meteorite if potassium-40 decayed from 80 g to 10 g? The half-life of potassium-40 is 1.3 billion years. 1.3 billion years 2.6 billion years 3.9 billion years 5.2 billion years PLS HELP URGENT

Answer 1

Answer:

3.9 billion years

Explanation:

The half-life of potassium-40 is the time it takes for half of it to decay.  

After one half-life, half of the original amount will remain.  

After a second half-life, half of that amount will remain, and so on.  

We can construct a table as follows:  

$\begin{array}{cccc}\textbf{No. of} &\textbf{Fraction} &\textbf{Mass}\\ \textbf{Half-lives} & \textbf{Remaining} & \textbf{Remaining/g}\\0 & 1 &80\\\\1 & \dfrac{1}{2} &40\\\\2 & \dfrac{1}{4} & 20\\\\3 & \dfrac{1}{8} & 10\\\\4 & \dfrac{1}{16} & 5\\\\\end{array}$

We see that the mass will drop to 10 g after three half-lives.

  1 half-life = 1.3 billion years

3 half-lives = 3.9 billion years

Answer 2

The age of the meteorite is 3.9 billion years.

Using the formula;

$N/No = (1/2)^t/t1/2$

Where;

N = Mass at time t = 10 g

No = initial mass present = 80 g

t = age of the meteorite

t1/2 = half life of potassium-40 =$1.3 * 10^9$ years

Substituting values;

$10/80 = (1/2)^ t/1.3 * 10^9$

$1/8 = (1/2)^ t/1.3 * 10^9$

Comparing both sides of the equation

$3 = t/1.3 * 10^9$

$t = 3 * 1.3 * 10^9$

$t = 3.9 * 10^9$ or 3.9 billion years

Hence, the age of the meteorite  is 3.9 billion years

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