Question

Manganese-52 has a half-life of 6 days. How many days would a scientist have to wait for the radioactivity to be 12.5% the starting amount?

6
12
18
24

Answer 1

Answer:

This is a list of radioactive nuclides (sometimes also called isotopes), ordered by half-life from shortest to longest, in seconds, minutes, hours, days, and years.

Answer 2

Given:

Manganese-52 has a half-life of 6 days.

To find:

How many days would a scientist have to wait for the radioactivity to be 12.5% the starting amount?

Calculation:

First of all , we need to find out the number of half-lifes passed to reach 12.5% of starting amount.

Let the number of half life be n :

$\sf \therefore \: { \bigg( \dfrac{1}{2} \bigg)}^{n} = 12.5\%$

$\sf \implies\: { \bigg( \dfrac{1}{2} \bigg)}^{n} = \dfrac{12.5}{100}$

$\sf \implies\: { \bigg( \dfrac{1}{2} \bigg)}^{n} = \dfrac{1}{8}$

$\sf \implies\: { \bigg( \dfrac{1}{2} \bigg)}^{n} = { \bigg( \dfrac{1}{2} \bigg)}^{3}$

$\sf \implies \: n = 3$

Now, number of days required is :

$\therefore \sf \: time \: required = t_{ \frac{1}{2} } \times n$

$\implies\sf \: time \: required = 6 \times 3$

$\implies\sf \: time \: required = 18 \: days$

So, required time to reach 12.5% is 18 days.