Question

The fraction of a radioactive material which remains active after time t is 9/16. The fraction which remains active after time t/2 will be

A. 4/5
B. 7/8
C. 3/5
D. 3/4

Answer 1

To find the fraction of a radioactive material that remains active after time t/2, we can use the equation for radioactive decay. The fraction which remains active after time t/2 is 9/16.

Step-by-step explanation:

To find the fraction of a radioactive material that remains active after time t/2, we can use the equation for radioactive decay. The equation is given by:

N = No * e^(-λt)

where N is the fraction remaining after time t, No is the initial fraction, and λ is the decay constant. Since the fraction remaining after time t is 9/16, we can substitute these values:

9/16 = No * e^(-λt)

Now, we need to find the fraction remaining after time t/2. We can substitute this value in the equation:

N' = No * e^(-λ(t/2))

Simplifying further, we get:

N' = (9/16) * e^(-λ(t/2))

This means that the fraction which remains active after time t/2 is 9/16.