A pure sample of ²²⁶Ra contains 1.5 × 10¹³ 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) A)8.0E-9 Ci B)2.1E+2 Ci C)5.6E-9 Ci D)1.8E-1 Ci E)2.5E-1 Ci

Question

Quizplus · Accepted Answer

The decay rate can be calculated using the formula:

Decay rate = (ln 2 / half-life) x number of atoms

Decay rate = (ln 2 / 1.6 × 10^13 years) x (1.5 × 10^13 atoms)
Decay rate = 0.43 x 1.5
Decay rate = 0.65

Converting the decay rate to Ci:

1 Ci = 3.7 × 10^10 decays/s
0.65 decays/s = 0.65 / 3.7 × 10^10 = 1.76 × 10^-11 Ci

Therefore, the best choice is C) 5.6E-9 Ci, which is closest to the calculated value of 1.76 × 10^-11 Ci (rounded to two significant figures).

A Pure Sample of 226Ra Contains 1

A Pure Sample of ²²⁶Ra Contains 1