Worked Example 3: Comparison with Reference Data

The table below shows calculated activities for selected fission products and actinides in irradiated fuel (based on Pickering CANDU fuel irradiated to 7.5 MWd/kg U). Use this to check your understanding of the approximations.

Isotope	Half-Life	Yield (%)	Activity at Discharge (Bq/kg U)	Activity at 1 yr (Bq/kg U)	Activity at 10 yr (Bq/kg U)	Notes
$^{85}$ Kr	10.76 y	0.29	$1.1 \times 10^{10}$	$1.0 \times 10^{10}$	$5.3 \times 10^{9}$	Noble gas; moderate half-life
$^{90}$ Sr	28.8 y	5.8	$1.6 \times 10^{11}$	$1.6 \times 10^{11}$	$1.2 \times 10^{11}$	Long-lived; bone-seeker
$^{95}$ Zr	64.0 d	6.5	$5.7 \times 10^{12}$	$1.5 \times 10^{9}$	~0	Short-lived; decays to $^{95}$ Nb
$^{95}$ Nb	35.0 d	---	$5.7 \times 10^{12}$	$3.4 \times 10^{9}$	~0	Daughter of $^{95}$ Zr
$^{131}$ I	8.02 d	2.9	$2.9 \times 10^{12}$	~0	~0	Very short-lived; thyroid hazard
$^{134}$ Cs	2.06 y	---	$3.0 \times 10^{10}$	$2.1 \times 10^{10}$	$1.1 \times 10^{9}$	Produced by neutron capture on $^{133}$ Cs
$^{137}$ Cs	30.17 y	6.2	$2.4 \times 10^{11}$	$2.3 \times 10^{11}$	$1.8 \times 10^{11}$	Long-lived; dominant gamma source
$^{144}$ Ce	284.9 d	5.5	$3.5 \times 10^{12}$	$1.4 \times 10^{11}$	$3.4 \times 10^{6}$	Moderate half-life
$^{239}$ Pu	24,110 y	---	$7.6 \times 10^{8}$	$7.6 \times 10^{8}$	$7.6 \times 10^{8}$	Alpha emitter; very long-lived
$^{241}$ Am	432.2 y	---	$1.2 \times 10^{7}$	$1.6 \times 10^{7}$	$5.9 \times 10^{7}$	Grows in from $^{241}$ Pu decay

Key observations from this table:

Short-lived isotopes ( $^{131}$ I, $^{95}$ Zr) dominate the activity at discharge but decay rapidly --- they are essentially gone after 1 year of cooling.
Medium-lived isotopes ( $^{144}$ Ce, $^{134}$ Cs) decay significantly over 1—10 years but are still present.
Long-lived isotopes ( $^{90}$ Sr, $^{137}$ Cs) barely decrease over 1 year and remain significant even after 10 years. These dominate the intermediate-term hazard.
Actinides ( $^{239}$ Pu, $^{241}$ Am) are essentially unchanged over 10 years and dominate the very long-term hazard.
$^{241}$ Am increases after discharge because it is continuously produced by the beta decay of $^{241}$ Pu ( $T_{1/2}$ = 14.3 y).

Common Mistakes --- Worked Example 3

Mistake How to Avoid It
Assuming all activities decrease after shutdown Remember: $^{241}$ Am increases because its parent $^{241}$ Pu continues to decay
Ignoring the difference between fission product and actinide half-lives Fission products: days to ~30 years. Actinides: thousands to millions of years
Confusing activity at discharge with activity after cooling Always state the cooling time when quoting an activity value

Mistake	How to Avoid It
Assuming all activities decrease after shutdown	Remember: $^{241}$ Am increases because its parent $^{241}$ Pu continues to decay
Ignoring the difference between fission product and actinide half-lives	Fission products: days to ~30 years. Actinides: thousands to millions of years
Confusing activity at discharge with activity after cooling	Always state the cooling time when quoting an activity value

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