To solve this problem, we need to use the formula for radioactive decay which is:

N = N0 * (1/2)^(t/T)

where:
N is the final quantity of the substance
N0 is the initial quantity of the substance
t is the time elapsed
T is the half-life of the substance

We are given:
N0 = 8.50 mg
N = 2.90 mg
T = 16.3 seconds

We need to solve for t.

First, divide N by N0:

2.90 mg / 8.50 mg = 0.3412

Then, take the logarithm base 0.5 of both sides of the equation:

log0.5(0.3412) = t / 16.3 seconds

Solving for t gives:

t = 16.3 seconds * log0.5(0.3412)

Using a calculator, we find that:

t ≈ 28.6 seconds

So, it would take approximately 29 seconds (rounded to two significant digits) for the sample to decay from 8.50mg to 2.90mg.

Question

To solve this problem, we need to use the formula for radioactive decay which is:

N = N0 * (1/2)^(t/T)

where:
N is the final quantity of the substance
N0 is the initial quantity of the substance
t is the time elapsed
T is the half-life of the substance

We are given:
N0 = 8.50 mg
N = 2.90 mg
T = 16.3 seconds

We need to solve for t.

First, divide N by N0:

2.90 mg / 8.50 mg = 0.3412

Then, take the logarithm base 0.5 of both sides of the equation:

log0.5(0.3412) = t / 16.3 seconds

Solving for t gives:

t = 16.3 seconds * log0.5(0.3412)

Using a calculator, we find that:

t ≈ 28.6 seconds

So, it would take approximately 29 seconds (rounded to two significant digits) for the sample to decay from 8.50mg to 2.90mg.

Knowee AI · Accepted Answer