Half life period of Ra226 is 1620 years calculate the decay rate of Ra226 in alpha particle per gram per sec
To calculate the decay rate of Ra226 in alpha particles per gram per second, we need to use the concepts of radioactive decay and decay constant.
The radioactive decay of Ra226 follows an exponential decay curve described by the equation:
N(t) = N₀ * e^(-λt)
Where:
N(t) is the number of radioactive atoms at time t,
N₀ is the initial number of radioactive atoms,
λ (lambda) is the decay constant, and
t is the time.
The decay constant (λ) is related to the half-life (T½) by the equation:
T½ = ln(2) / λ
Given that the half-life of Ra226 is 1620 years, we can calculate the decay constant:
T½ = 1620 years
ln(2) / λ = 1620 years
Solving for λ:
λ = ln(2) / 1620 years
Now, let's assume we have 1 gram of Ra226. We can calculate the number of radioactive atoms (N₀) using Avogadro's number (6.022 × 10^23 atoms/mol) and the molar mass of Ra226 (226 g/mol):
N₀ = (1 g / 226 g/mol) * (6.022 × 10^23 atoms/mol)
Next, to find the decay rate in alpha particles per gram per second, we need to find the rate of decay per second for 1 gram of Ra226. This can be calculated using the decay constant (λ) and the formula:
decay rate = N₀ * λ
Finally, we need to convert the decay rate from per second to per gram per second. Since we have 1 gram of Ra226, the decay rate in alpha particles per gram per second is equal to the decay rate per second.
Therefore, the decay rate of Ra226 in alpha particles per gram per second is:
decay rate = N₀ * λ
Note: The value calculated will give the average decay rate. The actual decay rate can vary due to the probabilistic nature of radioactive decay.