A one gram if 226 Ra has an activity of nearly 1Cl.determine the half life of 226Ra. The half life of 238U is 4.5×109year . what is the decay constant? Find the activity of 1g,of 238U

Answer 1

To determine the half life of 226 Ra, we use the formula:

A = A0 * (1/2)^(t/T)

where A = activity, A0 = initial activity, t = time elapsed, and T = half life.

We know that A0 = 1 Ci (we convert to Ci from mCi for convenience), and A = 0.5 Ci (since the activity is halved after one half life). We are given that we have 1 gram of 226 Ra, which has a molar mass of 226 g/mol. Therefore, we have 1/226 moles of 226 Ra.

Using the formula for activity:

A = λ * N

where N = number of radioactive atoms and λ = decay constant, we can solve for λ:

λ = A/N = (0.5 Ci) / [(6.022 x 10^23 atoms/mol) * (1/226 mol)] = 1.19 x 10^-8 s^-1

We use the half life formula again for 238 U:

T = 4.5 x 10^9 years = (ln 2) / λ

Solving for λ:

λ = (ln 2) / T = 1.54 x 10^-10 s^-1

Finally, we can find the activity of 1 gram of 238 U:

N = (1 g) / (238 g/mol) * (6.022 x 10^23 atoms/mol) = 2.54 x 10^21 atoms

A = λ * N = (1.54 x 10^-10 s^-1) * (2.54 x 10^21 atoms) = 0.40 Ci