Question

A 0.0116-g sample of a radioactive isotope with a half life of 1.3x10⁹ years decays at the rate of 2.9x10⁴ disintegrations per minute. Calculate the molar mass of the isotope.

Enter your answer in scientific notation. (g/mol)

Answer 1

dpm = decays/minute = # atoms lost/minute

Converting atoms lost/min to atoms lost/year:

(2.9 x 10^4 atoms lost/minute)
x (60 min / 1 hour)
x (24 hours / 1 day)
x (365 days / 1 year)

= 1.524 x 10^10 atoms lost/year

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Calculating atoms lost/half-life
from atoms lost/year:

(1.524 x 10^10 atoms lost/year)
x (1.3 x 10^9 years/half-life)

= 1.982 x 10^19 atoms lost/half-life

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Calculating mol sample lost/half-life
from atoms lost/half-life:

1.982 x 10^19 x 10^19 atoms lost/half-life
x (1 mol / 6.022 x 10^23 atoms)

= 3.290 x 10^-5 mol sample lost/half-life

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Fraction of sample lost after 1 half-life
1 - fraction of sample remaining after 1 half-life
= 1 - 0.50 (50%) = 0.50

Amount of sample lost/half-life:
(0.50) 0.0116 g = 0.0058 g sample lost/half-life

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Since we have g sample and mol of sample lost/half-life:

molar mass = (0.0058 g) / (3.290 x 10^-5 mol) = 176.29 g/mol

*** Answer: 176.3 g/mol ***