The mass of a radioactive element decays at rate given by m(t) = m0e-rt, where m(t) is the mass at any time t, m0 is the initial mass, and r is the rate of decay. Uranium-240 has a rate of decay of .0491593745. What is the mass of U-240 left after 10 hours, if the initial mass is 50 grams? A) 28.54387 g B) 30.58254 g C) 32.14286 g D) 32.68034 g

Question

The mass of a radioactive element decays at rate given by m(t) = m0e-rt, where m(t) is the mass at any time t, m0 is the initial mass, and r is the rate of decay.   Uranium-240 has a rate of decay of .0491593745. What is the mass of U-240 left after 10 hours, if the initial mass is 50 grams? A) 28.54387 g	 B) 30.58254 g	 C) 32.14286 g	 D) 32.68034 g

wolf1728 · Answer

Uranium - 240 has a half life of 14.1 hours Ending Amount = Beginning Amount / (2^n) where 'n' is the number of half-lives. (10/14.1) = 0.7092198582 Ending Amount = 50g / (2^0.7092198582) Ending Amount = 50 g / 1.6349197901 Ending Amount = 30.5825400757 g So it looks as if 'B' is definitely the answer. Here's a good page about half-life, decay, etc. http://1728.org/halflife.htm Has a calculator too.