A sample of radioactive waste has a half-life of 10 years and an activity level of 2 curies. After how many years will the activity level of this sample be 0.25 curie? a. 10 yearsb. 20 yearsc. 30 yearsd. 40 yearse. 80 years

c. 30 years

Step-by-step explanation:

The expression for half life of a radioactive substance is given as

λ/λ₁ = 2⁽ᵃ/ᵇ⁾ ... Equation 1

Where λ₁ = remaining sample, λ = original sample, a = Total disintegration time, b = half life.

Given: λ = 2 curies, λ₁ = 0.25 curies, b = 10 years.

Substituting these values into equation 1

2/0.25 = 2⁽ᵃ/¹⁰⁾

8 = 2⁽ᵃ/¹⁰⁾

2³ = 2⁽ᵃ/¹⁰⁾

Since the base in both side of the equation is the same, we can equate the base.

3 = a/10

a/10 = 3

a = 10*3

a = 30 years.

Thus it will take 30 years for the activity level of the sample to be 0.25 curie

The right option is c. 30 years