Question 330: Atoms & Nuclei

Question

The decay constant for a radioactive nuclide is 1.5 $$	imes$$ 10$$^{-5}$$ s$$^{-1}$$. Atomic weight of the substance is 60 g mole$$^{-1}$$, ($$N_A=6	imes10^{23}$$). The activity of 1.0 $$\mu$$g of the substance is ___________ $$	imes$$ 10$$^{10}$$ Bq.

Accepted Answer

The activity of a radioactive substance is defined as the rate of decay or disintegration of the substance. It is given by the following formula:
$$A = \lambda N$$
where $A$ is the activity, $\lambda$ is the decay constant, and $N$ is the number of radioactive atoms present.
We can use this formula to find the activity of 1.0 $\mu$g (or $10^{-6}$ g) of the substance. First, we need to find the number of radioactive atoms present in 1.0 $\mu$g of the substance. We can use the following formula to do this:
$$N = \frac{m}{M} N_A$$
where $m$ is the mass of the substance, $M$ is its molar mass, and $N_A$ is Avogadro's number.
Substituting the given values, we get:
$$N = \frac{1.0 	imes 10^{-6} \, 	ext{g}}{60 \, 	ext{g/mol}} 	imes 6 	imes 10^{23} \approx 10^{16} 	ext{ atoms}$$
Now, we can use the formula for activity:
$$A = \lambda N = (1.5 	imes 10^{-5} \, 	ext{s}^{-1}) (10^{16}) = 1.5 	imes 10^{11} \, 	ext{Bq}$$
Therefore, the activity of 1.0 $\mu$g of the substance is 15 $	imes$ 10$^{10}$ Bq.

Atoms & Nuclei

The decay constant for a radioactive nuclide is 1.5 $\times 10^{-5} s^{-1}. Atomic weight of the substance is 60 g mole^{-1}, (N_A=6\times10^{23}). The activity of 1.0 \mug of the substance is ___________ \times 10^{10}$ Bq.

Integer / Numeric Answer Type