Americium is the only synthetic element to have found its way into the household

Question

Americium is the only synthetic element to have found its way into the household, where one common type of smoke detector contains about 0.2 microgram of 241Am95 as a source of ? particles. The ? particles ionize the air in the space between two electrodes and this permits a small constant current to flow between the electrodes. Smoke that enters the chamber absorbs the alpha particles, which reduces the ionization and interrupts this current, setting off the alarm. The half-life of 241Am95 is 432 years.

(a) How many ? particles are emitted per second by 0.2 microgram of 241Am95?

(b) What is the mass of a mole of 241Am95?

(c) Suppose we start with a mole of 241Am95. After 32,400 years, what is the number of atoms that remain?

Explanation / Answer

0.2 x 10^-6 gram of americum contains 0.2 x 10^-6 x Avagadro number / 241 = 5 x 10^14 atoms.

= ln2 / t1/2 = 0.0016 year-1 = 5.09 x 10-11 sec-1.

a) Activity = N = 5 x 10^14 x 5.09 x 10-11 = 25439 -Decays.

b) 1 mole of 241Am95 weighs 241 grams.

c) N = Noe-t = 6.023 x 10^23 x e-0.0016 x 32400 = 18.4 18 atoms remain.

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