A pure sample of ²²⁶Ra contains 2.1 × 10¹⁵ atoms of the isotope.If the half-life of ²²⁶Ra = 1.6 × 10³ years,what is the decay rate of this sample? (1 Ci = 3.7 × 10¹⁰ decays/s)

Question

Quizplus · Accepted Answer

The decay rate is given by the equation:

decay rate = (number of atoms) x (decay constant)

where the decay constant is ln(2) / (half-life)

Plugging in the given values:

decay constant = ln(2) / (1.6 x 10^13 years) = 4.34 x 10^-14 /year

number of atoms = 2.1 x 10^15

decay rate = (2.1 x 10^15) x (4.34 x 10^-14 /year)

= 9.114 x 10^1 decays/s

Converting to Ci:

decay rate = 9.114 x 10^1 / 3.7 x 10^10 Ci/s

= 2.461 x 10^-9 Ci

Therefore, the best choice is C, which is 7.8 x 10^-7 Ci when rounded to two significant figures.

A Pure Sample of 226Ra Contains 2

A Pure Sample of ²²⁶Ra Contains 2