Original Sample of Nuclides

Please find answers to your questions attached. Please confirm if the isotope of Calcium in question 12 is Ca-45. If so, then the calculated value agrees with the literature value.

11. The equation for radioactive decay is NT = N0 × e−kt
Where NT is the Amount remaining after a time t (minutes) and k is the radioactive decay constant
Taking the logarithm of both sides with respect to e, you can rewrite the equation as
ln (N_32/N_0) = k×T1/2
and from which we get ln (0.5) = k × 32.....................................................(1)
since 32 minutes is the half-life
Then we also have ln (N_180/N_0) = k×180....................................................(2)
Where we need to find N_180/N_0 where N180 refers to the amount left after 180 minutes or 3 hours.
Dividing (2) by (1) we get ln ln (N_180/N_0) = 180 × 32 × (ln 5) = -3.899
Which gives (N_180/N_0) = 0.02026
OR only 2.03% of the original amount is left after 180 min or 3 hours.

12. Using the same equation for radioactive decay
ln (N_t/N_0) = −k×t
where k is the decay constant and t is the time
For the half-life, N_t/N_0 = 0.5 and k = 4.23 × 10−3 day−1
And t1/2 = ln 0.5/4.23 × 10−3 day−1 = 163.86 days for the 45-Ca isotope.

13. PCl3 + 3H2O → H3PO3 + 3HCl

14. P4O10 + 6H2O → 4H3PO4

15.
[Co(NH3)4Cl2]Br
Tetraamminedichlorocobalt(III) bromide

16. Coordination of Cobalt(III) = 6

17. Coordination Geometry = Octahedral, or more correctly, distorted Octahedral.

18. Geometrical iosmerism may be exhibited by this complex—the two Cl ligands may be trans (opposite) to each other OR the two Cl ligands may be cis to each other (adjacent)

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