Question

studying for my final, help

13) (2 pts) The isotope, tritium, has a half-life of 12.3 years and atomic mass 3.016 amu. Assume we have 10 kg of the substance. What will be the initial decay rate, at t=0 (in decays/s)? a. 1.09 x 1014 decays/s b. 1.8 x 10-9 decays/s c. 5.6 x 108 decays/s d. 3.6 x 1018 decays/s e. 3.6 x 1017 decays/s

Answer 1

Hi,

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Given that,

Initial mass of tritium, m = 10 kg = 10⁴ g

Molar mass of tritium, M = 3 amu= 3 g/mol

Therefore, initial no.of moles of tritium is given by,

n = m M 104 = 3 alma = 3.333 x 10 moles "

Therefore, Initial no.of atoms:

No=nx NA = 3.333 x 10' moles x 6.022 x 1023

::N= 2.007 X 1027

Also, given that, Half life of tritium,

t1/2 = 12.3 yrs = 12.3 yrs x 31536 x 103 s/year

..t1/2 = 387892800 s

Therefore, Initial rate is given by,

0.693 R=N. 1/2/

:: R=2.007 x 1027 x | 0.693 387892800 s)

::R= 3.59 x 1018 decays/sec

::R~ 3.6 x 1018 decays/sec

Therefore, The correct option is Option (d) 3.6 x 10¹⁸ decays/s

Best of luck for your finals!
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