Answer to Question #163784 in Physics for John

Question

Sodium 24 is a radioactive isotope with a half-life of 14.8hrs. Calculate

a) The decay constant of the isotope

b) The number of atoms in a 1.0mg sample of this isotope.

c) The activity of the 1.0mg pure sample of the isotope.

d) The activity of such a sample exactly 24 hours later

Answer 1

a)

$$\lambda=\frac{\ln{2}}{14.8}=0.0468\ h^{-1}$$

b)

$$N=\frac{1\cdot 6.02\cdot10^{23}}{24000}=2.51\cdot10^{19}$$

c)

$$A=(0.0468)2.51\cdot10^{19}=3.26\cdot10^{14}\frac{decay}{h}$$

d)

$$A(24)=3.26\cdot10^{14}e^{-0.0468(24)}=1.06\cdot10^{14}\frac{decay}{h}$$