# Homework Help: Nuclear activity

1. Nov 18, 2008

### Confundo

Didn't really have any idea when I started to write the problem, but I think I've managed to work it out now posting for clarification.
1. The problem statement, all variables and given/known data

Estimate the time it will take to produce a 100 μCi source of 36Cl by irradiating 1g of natural nickel chloride (molecular weight 129.6) in a neutron flux of 1014 cm-2s-1. The cross section for neutron capture on 35Cl is 43 b and the half-life of 36Cl is 3 x 105 years. 75.8% of natural chlorine consists of 35Cl.

2. Relevant equations

Number of 35-Cl atoms in 1g of NaCl2 is
$$N = 2x0.758xN_A/molecular weight = 7.04x10^{21}$$
$$A(t) = \lambda N = P(1 - e^{-\lambda t} \approx P\lambda t$$
$$t = \frac{A(t)}{P\lambda} = \frac{A(t)t_{1/2}}{ln 2 x \Omega x F x N}$$

$$F = incident flux, A(t) = activity, \Omega = cross section for neutron capture$$

3. The attempt at a solution

$$F = 10^{14} cm^{-2}s^{-1}$$
$$t_{1/2} = 3.16x10^7 x 3x10^5 = 9.48x10^12 s$$
$$\Omega = 43x10^-24 cm$$
$$A(t) = 100\mu Ci = 3.7x10^6 Bq$$

Putting in the numbers gives 1.67164x10^6 seconds = 19.35 days

Didn't really have any idea when I started to write the problem, but I think I've managed to work it out now posting for clarification.