Americium-241 is widely used in smoke detectors. The radiation released by this element ionizes particles that are then detected by a charged-particle collector. The half-life of 241Am is 432 years, and it decays by emitting alpha particles. How many alpha particles are emitted each second by a 5.54-g sample of 241Am

Explanation:

Half life T is 432 years .

432 years = 432 x 365 x 24 x 60 x 60 s

= 1.36 x 10¹⁰ s .

No of atoms in 5.54 g of sample of Am N= 6.02 x 10²³ x 5.54 / 241

N = 138.38 x 10²⁰ atoms .

disintegration constant λ = .693 / half life

λ =  .693 / 1.36 x 10¹⁰ s .

= .51 x 10⁻¹⁰ .

dN / dt = λN

= .51 x 10⁻¹⁰  x  138.38 x 10²⁰

= 70.57 x 10¹⁰ per second.

No of particles emitted = no of disintegration per second

No of particles emitted =  70.57 x 10¹⁰ per second.