Question

How much of a 500 gram sample of potassium-42 is left after
62 hours? The half-life of K-42 is 12.4 hours?

Answer 1

Answer:

The correct answer is - 15.625

Explanation:

The half-life is the time it takes to decay half value or quantity of its initial quantity or value. It is given that,

The half-life of K-42 = 12.4 hours

The initial value of K-42 = 500 gm

After 62 hours the value of k-42 = ?

The number of half cycle = 62*1/12.4 = 5,

therefore it will have 5 half-lives

initial - 500

1st half life - 500/2 = 250

2nd - half life - 250/2 = 125

3rd half life - 125/2 = 62.5

4th half life - 62/2 = 31.25

fifth half life - 31.25/2 = 15.625

Thus, the correct answer is =15.625g

Answer 2

15.625 g of  a 500 gram sample of potassium-42 with 12.4 hours of Half -life is left after 62 hours.

The half-life is the time after which half of the initial quantity of a radioactive substance is left .

Given here,  

The half-life of K-42 = 12.4 hours  

The initial quantity of K-42 = 500 gm  

The final quantity after 62 hours = ?  

The number of half cycle

$\bold { = 62\times \dfrac 1{12.4} = 5,}$  

Thus the number of half life cycles in 62 hours is 5,

 

After 1 half life $\bold {= \dfrac {500}{2} = 250}$  

After 2 half lives $\bold {= \dfrac {250}{2} = 125}$  

After 3 half lives $\bold {= \dfrac {125}{2} = 62.5}$  

After 4 half lives  $\bold {= \dfrac {62.5}{2} = 31.25}$  

After 5 half lives $\bold {= \dfrac {31.25}{2} = 12.625}$  

15.625 g of  a 500 gram sample of potassium-42 with 12.4 hours of Half -life is left after 62 hours.

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