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 that has passed
T is the half-life of the substance

In this case, we have:
N0 = 3.80 mg
t = 7.86 minutes
T = 2.23 minutes

Substituting these values into the formula, we get:

N = 3.80 mg * (1/2)^(7.86/2.23)

Calculating the exponent first:

7.86/2.23 = 3.52

So the equation becomes:

N = 3.80 mg * (1/2)^3.52

Calculating the value of (1/2)^3.52 gives approximately 0.0907.

So, N = 3.80 mg * 0.0907 = 0.34466 mg

Rounding this to two significant digits gives 0.34 mg.

So, after 7.86 minutes, there would be approximately 0.34 mg of the Tin-129 sample left.

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 that has passed
T is the half-life of the substance

In this case, we have:
N0 = 3.80 mg
t = 7.86 minutes
T = 2.23 minutes

Substituting these values into the formula, we get:

N = 3.80 mg * (1/2)^(7.86/2.23)

Calculating the exponent first:

7.86/2.23 = 3.52

So the equation becomes:

N = 3.80 mg * (1/2)^3.52

Calculating the value of (1/2)^3.52 gives approximately 0.0907.

So, N = 3.80 mg * 0.0907 = 0.34466 mg

Rounding this to two significant digits gives 0.34 mg.

So, after 7.86 minutes, there would be approximately 0.34 mg of the Tin-129 sample left.

Knowee AI · Accepted Answer