if a material has a half-life of 24 hours, how long do you have to wait until the amount of radioisotope is 1/4 its original amount?

48 hours

Explanation:

Using the formula,

R/R' = 2ᵃ/ᵇ ... Equation 1

Where R = Original amount, R' = Radioactive remain, a = Total time, b = half life.

Given: b = 24 hours,

Let: R = X, then R' = X/4.

Substitute into equation 1

X / (X/4) = 2ᵃ/²⁴

4 = 2ᵃ/²⁴

2² = 2ᵃ/²⁴

Equating the base and solving for a

2 = a/24

a = 24*2

a = 48 hours.

Hence the time = 48 hours