Asked by Garou
A radioactive isotope has a decay constant of 9.68E-03 /s. Calculate the time taken for three quarters of a sample of the isotope to decay.
Answers
Answered by
Garou
list of prime numbers from 50 through 75
Answered by
GPT 3.5
The decay constant, denoted by λ, is given as 9.68E-03 /s.
The decay of a radioactive sample can be modeled using the equation: N(t) = N0 * e^(-λt),
where N(t) is the number of radioactive atoms remaining at time t, N0 is the initial number of radioactive atoms, λ is the decay constant, and e is the base of the natural logarithm.
We need to calculate the time taken for three-quarters (3/4) of the sample to decay, which means we want to find t when N(t) = 1/4 * N0.
1/4 * N0 = N0 * e^(-λt).
Dividing both sides of the equation by N0, we get:
1/4 = e^(-λt).
To isolate t, take the natural logarithm (ln) of both sides:
ln(1/4) = ln(e^(-λt)).
Using the property of logarithms, ln(a^b) = b * ln(a), we have:
ln(1/4) = -λt * ln(e).
Since ln(e) is equal to 1, we can simplify the equation further:
ln(1/4) = -λt.
Now, we solve for t:
-λt = ln(1/4).
Dividing both sides by -λ, we get:
t = ln(1/4) / (-λ).
Plugging in the given decay constant, λ = 9.68E-03 /s, we can now calculate t:
t = ln(1/4) / (-9.68E-03 /s).
Using a calculator, evaluate ln(1/4) / (-9.68E-03) to get the time taken for three-quarters of the sample to decay.
The decay of a radioactive sample can be modeled using the equation: N(t) = N0 * e^(-λt),
where N(t) is the number of radioactive atoms remaining at time t, N0 is the initial number of radioactive atoms, λ is the decay constant, and e is the base of the natural logarithm.
We need to calculate the time taken for three-quarters (3/4) of the sample to decay, which means we want to find t when N(t) = 1/4 * N0.
1/4 * N0 = N0 * e^(-λt).
Dividing both sides of the equation by N0, we get:
1/4 = e^(-λt).
To isolate t, take the natural logarithm (ln) of both sides:
ln(1/4) = ln(e^(-λt)).
Using the property of logarithms, ln(a^b) = b * ln(a), we have:
ln(1/4) = -λt * ln(e).
Since ln(e) is equal to 1, we can simplify the equation further:
ln(1/4) = -λt.
Now, we solve for t:
-λt = ln(1/4).
Dividing both sides by -λ, we get:
t = ln(1/4) / (-λ).
Plugging in the given decay constant, λ = 9.68E-03 /s, we can now calculate t:
t = ln(1/4) / (-9.68E-03 /s).
Using a calculator, evaluate ln(1/4) / (-9.68E-03) to get the time taken for three-quarters of the sample to decay.
Answered by
GPT 3.5
The prime numbers from 50 through 75 are:
53, 59, 61, 67, 71, 73
53, 59, 61, 67, 71, 73