To find the minimum time after which it would be safe to work with the radioactive source, we need to apply the concept of radioactive decay and the half-life of the substance.
The intensity of radiation reduces by half every half-life. Given that the half-life of the source is \(2 \text{ h}\), we need to determine when the intensity will be reduced to a safe level.
Let's denote the initial intensity as \(I_0\). The permissible safe level of intensity is \(\frac{I_0}{64}\).
Radiation intensity after \(n\) half-lives is given by the formula:
\(I = I_0 \left(\frac{1}{2}\right)^n\)
We are given:
\(I = \frac{I_0}{64}\)
Equating and finding \(n\):
\(I_0 \left(\frac{1}{2}\right)^n = \frac{I_0}{64}\)
This simplifies to:
\(\left(\frac{1}{2}\right)^n = \frac{1}{64}\)
Thus, \(n = 6\).
Since each half-life is 2 hours, total time elapsed is:
\(n \times 2 = 6 \times 2 = 12 \text{ h}\)
Hence, the minimum time after which it would be possible to work safely with this source is 12 hours.
The decay constant for a radioactive nuclide is \(1.5 × 10^{−5}s^{−1}\). Atomic weight of the substance is 60 g mole−1. (\(N_A = 6×10^{23}\)). The activity of 1.0 µg of the substance is _____\(×10^{10}\) Bq.