Question

calculate the number of alpha particles emitted per second from 1g of radium.assume half life of radium is 1600 years.calculate the volume of helium gas produced by 1g of radium in 1 year

Answer 1

Answer on Question#38467, Physics, Nuclear Physics

Question:

Calculate the number of alpha particles emitted per second from 1g of radium. Assume half-life of radium is 1600 years. Calculate the volume of helium gas produced by 1g of radium in 1 year.

Answer:

The equation that describes decay is (for $\Delta t \ll t_{\frac{1}{2}}$):

$$\Delta N = \lambda N \Delta t$$

where $\lambda$ is the decay constant of radionuclide related to its half-lives $t_{\frac{1}{2}}$ by

$$\lambda = \frac{\ln(2)}{t_{\frac{1}{2}}}$$

Number of atoms in 1g of radium equals:

$$N = N_A \frac{m}{M}$$

where $M$ is molar mass, $N_A$ is Avogadro constant.

Therefore:

$$\Delta N = \frac{\ln(2)}{t_{\frac{1}{2}}} N_A \frac{m}{M} \Delta t = 3.7 * 10^{10}$$

Answer: $3.7 * 10^{10}$

For 1 year:

$$\Delta N = \frac{\ln(2)}{t_{\frac{1}{2}}} N_A \frac{m}{M} \Delta t = 3.2 * 10^{15}$$

Volume equals:

$$V = V_m \frac{\Delta N}{N_A} = 22.4 \frac{l}{mol} \frac{3.2 * 10^{15}}{6.02 * 10^{23} \frac{1}{mol}} = 1.2 * 10^{-7} l$$

Answer: $1.2 * 10^{-7} l$