The activity of radioactive substance reduced from 2000Bq to 1000Bq in 10^6sec.what is the decay constant
The decay constant can be calculated using the formula:
λ = (ln(N0/Nt))/t
Where:
λ = decay constant
N0 = initial activity
Nt = final activity
t = time interval
Substituting the given values:
N0 = 2000 Bq
Nt = 1000 Bq
t = 10^6 sec
λ = (ln(2000/1000))/10^6
λ = 6.93 x 10^-7 s^-1
Therefore, the decay constant is 6.93 x 10^-7 s^-1.
To find the decay constant, we can use the radioactive decay equation:
N(t) = N₀ * e^(-λt)
Where:
N(t) is the final amount of the radioactive substance after time t,
N₀ is the initial amount of the radioactive substance,
e is the mathematical constant approximately equal to 2.71828,
λ (lambda) is the decay constant,
t is the time elapsed.
We are given that the initial amount of the radioactive substance is 2000Bq, and the final amount is 1000Bq. The time elapsed is 10^6 seconds (1,000,000 seconds).
Plugging these values into the equation, we have:
1000 = 2000 * e^(-λ * 10^6)
Dividing both sides by 2000:
0.5 = e^(-λ * 10^6)
Taking the natural logarithm of both sides:
ln(0.5) = -λ * 10^6
Dividing both sides by -10^6:
-ln(0.5) / 10^6 = λ
Calculating the value:
λ ≈ -0.000000693 s^(-1)
Therefore, the decay constant is approximately -0.000000693 s^(-1).