Question

The half-life of radium-226 is 1620 years. How much of one gram of radium-226 will remain unchanged after four half-lives?

Answer 1

The correct answer is option C : 0.0625g of one gram of radium-226 will remain unchanged after four half-lives. 

Answer 2

Answer:

0.0625 g

Step-by-step explanation:

Given : The half-life of radium-226 is 1620 years.

Formula of half life:

$P(t) =P_0(\frac{1}{2})^\frac{t}{1620}$

So. $P_0$ = initial amount

P(t)= mass of radioactive material at time interval (t)

1 half life = 1620 years

4 half lives = 4 * 1620

So, t = 4 * 1620

Substituting the values :

$P(t) =1 (\frac{1}{2})^\frac{4\times 1620 }{1620}$

$P(t) = (\frac{1}{2})^4$

$P(t) = \frac{1}{16}$

$P(t) =0.0625$

Hence  0.0625 g of one gram of radium-226 will remain unchanged after four half-lives

Option C is correct.