To solve this problem, we need to use the formula for exponential decay which is N = N0 * (1/2)^(t/T), where:

N is the final amount of the substance,
N0 is the initial amount of the substance,
t is the time that has passed, and
T is the half-life of the substance.

In this case, we want to find N/N0, the fraction of the substance that remains after time t. We know that t = 37.3 seconds and T = 14.10 seconds.

So, we can substitute these values into the formula:

N/N0 = (1/2)^(37.3/14.1)

Calculating the exponent first:

37.3/14.1 = 2.645

Then, calculate the base to the power of the exponent:

(1/2)^2.645 = 0.208

To express this as a percentage, we multiply by 100:

0.208 * 100 = 20.8%

So, approximately 20.8% of the Indium-116 sample would be left after 37.3 seconds.

Question

To solve this problem, we need to use the formula for exponential decay which is N = N0 * (1/2)^(t/T), where:

N is the final amount of the substance,
N0 is the initial amount of the substance,
t is the time that has passed, and
T is the half-life of the substance.

In this case, we want to find N/N0, the fraction of the substance that remains after time t. We know that t = 37.3 seconds and T = 14.10 seconds.

So, we can substitute these values into the formula:

N/N0 = (1/2)^(37.3/14.1)

Calculating the exponent first:

37.3/14.1 = 2.645

Then, calculate the base to the power of the exponent:

(1/2)^2.645 = 0.208

To express this as a percentage, we multiply by 100:

0.208 * 100 = 20.8%

So, approximately 20.8% of the Indium-116 sample would be left after 37.3 seconds.

Knowee AI · Accepted Answer