The activity of radioactive substance reduced from 2000Bq to 1000Bq in10^6sec.what is the decay constant
The decay constant (λ) can be calculated using the equation:
N = N0 * e^(-λt)
where N is the final activity (1000 Bq), N0 is the initial activity (2000 Bq), t is the time (10^6 sec), and e is the mathematical constant 2.71828...
Substituting the values given, we get:
1000 = 2000 * e^(-λ*10^6)
Simplifying, we get:
e^(-λ*10^6) = 0.5
Taking natural logarithm on both sides, we get:
ln(e^(-λ*10^6)) = ln(0.5)
Simplifying, we get:
-λ*10^6 = -0.693
Dividing by 10^6, we get:
λ = 6.93 * 10^-7 s^-1
Therefore, the decay constant is 6.93 * 10^-7 s^-1.
To find the decay constant, we can use the following equation:
N = N0 * e^(-λt)
Where:
N is the final activity (1000 Bq)
N0 is the initial activity (2000 Bq)
λ is the decay constant (to be determined)
t is the time interval (10^6 seconds)
We can rearrange the equation to solve for λ:
λ = -ln(N/N0) / t
Substituting the given values, we have:
λ = -ln(1000/2000) / (10^6 seconds)
Simplifying,
λ = -ln(0.5) / (10^6 seconds)
Using a scientific calculator or computer program, we can find the natural logarithm of 0.5 and divide it by 10^6 seconds to calculate the decay constant. After evaluating the expression, the resulting decay constant can be obtained.