Cyberphysics - Question on Radioactive decay



		Question on Radioactive decay
		A speck of uranium dust contains 10¹⁴ atoms. It has a mass of 3.95 x 10^-8g. The half life of Uranium 238 is 4.5 x 10⁹ years. It is inhaled and lodges in the lung. What is the initial rate of disintegration of the dust spec? 3.95 x 10^-8g uranium contains 10¹⁴atoms N₀ = 10¹⁴atoms dN/dt = ? half life = 4.5 x 10⁹ years = 4.5 x 10⁹ x 365.25 days = 4.5 x 10⁹ x 365.25 x 24 hours = 4.5 x 10⁹ x 365.25 x 24 x 60 hours = 4.5 x 10⁹ x 365.25 x 24 x 60 x 60 seconds = 1.42 x 10¹⁷ seconds l = - ln2/half life = - 0.693/(1.42 x 10¹⁷) = - (- 0.693 /(1.42 x 10¹⁷)) x 10¹⁴ = 0.693 x 10^{14 )}/ 1.42 x 10¹⁷ = 4.9 x 10^-4 s^-1 = 1.8 h^-1 = 42 day^-1 = 15,400 year^-1