How much krypton-85 leaks into the atmosphere each year?

A recent paper estimated krypton-85 activity in a cubic metre of air at 1.31 Bq. See: Variability of atmospheric krypton-85 activity concentrations observed close to the ITCZ in the southern hemisphere.

Measurements between August 2007 and May 2010 covered three wet seasons. The mean activity concentration of krypton-85 measured during this period was 1.31±0.02Bqm^-3. A linear model fitted to the average monthly data, using month and monsoon as predictors, shows that krypton-85 activity concentration measured during the sampling period has declined by 0.01Bqm^-3 per year.

The measurement, done over 3 years found krypton-85 levels were stable. neither increasing nor decreasing by much. I'll assume that krypton-85 released in balanced by decay.

How much krypton-85 could there be in the atmosphere?

The surface density of air = 1.217 kg/m³
Total mass of the earth's atmosphere = 5.1 × 10¹⁸ kg
Let's assume 1.217 kg/m³ of surface air has a krypton-85 activity of 1.31 Bqm^-3
Let's next assume that krypton-85 activity is the same throughout the air. This will overestimate krypton-85 because its heavier than air. It's almost twice as heavy as carbon dioxide.
Proceeding with our over-estimation. Total activity of Kr-85 in all the atmosphere:
= (1.31 Bqm^-3) × (5.1 × 10¹⁸ kg) / 1.217 kg/m³
= 5.49 × 10¹⁸ Bq

The Specific Activity of krypton-85:
= 400 (Ci/g) [Ci = Curie]
= 1.48 × 10¹³ Bq/g

So our over-estimation for the amount Kr-85 in earth's atmosphere:
= (5.49 × 10¹⁸ Bq) / (1.48 × 10¹³ Bq/g)
= 3.71 × 10⁵ g
= 371 kg

How much krypton-85 is made each year

Krypton-85 is about 0.3% of fission products. Let's assume there is 400 GWe of nuclear reactor capacity on earth. That a 1GWe NPP operating over a year produces just less than 1 ton of fission products. Let's call that 400 tons fission products per year for all the world's reactors. That's works out at 1200 kg of krypton-85 made each year.

But all of krypton-85 does not leak into the atmosphere. Most of it is in sealed casks. The amount that leaks must be about the same as the amount that decays.

t_½(Kr-85) = 10.7 years
λ(Kr-85) = 0.693 / 10.7 years = 0.064766355 years^-1

How much Kr-85 is left after 1 year:

Fractional proportion at time t = N(t) / N(0) = e^{-λ t}
= e^{-0.064766355 years¯¹ × 1 years}
= e^-0.064766355
= 0.93728643

How much Kr-85 leaks?:

= 371 kg × (1 - 0.93728643)
= 23.27 kg

Note: Estimating the amount of fission products made/year

This depends upon the total capacity of all the world's nuclear reactors. There are:

• 435 commercial nuclear power reactors operable in 31 countries, with about 375 GWe of total capacity.
• 180 nuclear reactors power some 140 ships and submarines.
• 240 research reactors

I'll assume an average of 50Me per research and/or sea vessel reactor. So 420 × 50 = 21 GWe of small reactors. Let's round that to 400 GWe capacity for all reactors.