If a radioactive isotope that was injected into your bloodstream has a half-life of 5 hours, how many hours do you have to wait before the amount of this isotope in your body is 1/16 its original amount?

20 hours

Explanation:

Using

R/R' = 2ᵃ/ᵇ ... Equation 1

Where R = Original amount of radioactive isotope, R' = Amount of radioactive isotope after disintegration, a = Total disintegration time, b = half life.

Note: The Fraction of original amount of radioactive isotope is 1.

Given: R = 1, R' = 1/16, b = 5 hours

Substitute into equation 1

1 / (1/16) = 2ᵃ/⁵

16 = 2ᵃ/⁵

2⁴ = 2ᵃ/⁵

Equation the base

4 = a/5

a = 4*5

a = 20 hours

Hence the time = 20 hours

Total time = 20 hours

Explanation:

Half life is the amount of time it takes for a substance to decay tohalf of it's original amount.

Half life = 5 hours.

We have to obtain the number of half lives to get the time required.

1st half life = 1/2

2nd half life = 1/4

3rd half life = 1/8

4th half life = 1/16

So ffour half lives.

Total time = number of half lives * Time of half life

Total time = 4 * 5

Total time = 20 hours