Question

1. A sample contains 2x10^20 atoms of an isotope that decays with a half-life of 2.2 years. How many undecayed atoms are left after 7.9 years?

A. 5.6x10¹⁹ Atoms

B. 1.7x10¹⁹ Atoms

C. 1.8x10²⁰ Atoms

D. 1.3x10¹⁸ Atoms

Answer 1

sample contains 2x10^20 atoms

half-life of 2.2 years

So we have the relation as

A(t) = Ao × (1/2)t/t(1/2)

Here A(t) denotes amount left after t years;
A0 - the initial quantity of the substance that will undergo decay;
t1/2 - the half-life of the decaying quantity

Non substitution of values we will get

A(7.9 years) = 1.659811 × 10^19 atoms .... this much atom has been decayed and we have to find how much atom left undecayed so that,

undecayed atoms are left after 7.9 years = 2× 10^20 - 1.659811 × 10^19 = 1.834018897 × 1020 atoms