Short answer:

if the half life of a certain element is 2 hours, how long will

ittake for 93.75% of a certain amount of the element to

radioactivitydecay?

It will take 8 hours for the element to decay

Explanation:

Half life: This is the time taken for half the total number of atoms in a given sample of a radioactive element to decay.

λ/λ₁ = 2 (ᵃ/ⁿ) ... Equation 1

λ₁ = radioactive remain, λ = original amount, a = total disintegration time, n = half life.

Given: λ = 100%, λ₁ = 100-93.75 = 6.25%, n = 2 hours.

Substituting these values into equation 1,

100/6.25 = 2 (ᵃ/²)

16 = 2 (ᵃ/²)

2⁴ = 2 (ᵃ/²)

Equating the base from both side of the equation,

4 = a/2

a = 4*2

a = 8 hours.

Thus it will take 8 hours for the element to decay