Radioactive decay heat calculator

Release notes

Version 1.0. The Ionactive Radioactive decay heat calculator is designed to illustrate the heat generated during the process of radioactive decay. During decay alpha, beta and gamma rays may be emitted (depending on the radionuclide) and the interaction of these radiations with materials will result in an energy transfer which yields heat. The heat output depends on a number of factors including the type of radiation emitted, the energy of the radiations, the activity of the source, the half-life and specific activity. A common theme is that high activity will be present (GBq → TBq → PBq), and due to lower activity being involved in many common uses of radioactive material, the heat aspect often goes unnoticed. 

Examples of heat generation from radioactive materials include:

• Geothermal heating deep in the earth from uranium, thorium and potassium radioisotopes.
• Reactor decay heat from fission products (following reactor shutdown and during the storage of spent nuclear fuel.
• The release of thermal energy from the storage and use of High Activity Sealed Sources (HASS) like Co-60, often with activities in the multi PBq range.
• The use of Sr-90 (high energy beta emitters) in RTGs (radio-thermoelectric generator) where the thermal  energy is converted to electrical energy.
• The use of Pu-238 (alpha emitter) in higher power RTG's (e.g. to power space probes) and lower power applicators such as pacemakers).

In many of the examples the heat produced is desirable, whereas in the case of using Co-60 sources (for industrial irradiation), the heat produced is adventitious and must be removed by ventilation and / or water cooling. 

In our calculator, the output is based on W/ per unit activity (where 1 W = 1 J/s). The unit activity is either the Bq (becquerel) or the Ci (Curie)  - where 1 Ci  = 37 GBq. The calculator uses standard W/Bq data from MicroShield. 

The basic output of the calculator is in W, where we initially assume a Watt is a Watt - so do not account for efficiency of energy conversion. The idea of this is just to provide the user with some raw numbers to understand the magnitude of thermal output (idealistic). 

The user can then go deeper and :

• Heat up a volume of water , determining how long it would take to reach a desired temperature.
• Charge a mobile phone.
• Operate an RTG and power some lights (LEDs). 

For this calculator we are not considering losses (which could be important when designing facilities or applications). For example, in the water heating example we are not considering heat loss to the outside environment around the water body. 

The calculator is fairly simple - what follows is a basic run-through the functions.

Radionuclide  - choose from 20 radionuclides. We have designated these as cool, warm and hot but this is someone arbitrary (e.g. K-40 is designated as cool on a Bq/g and half life basis, but over geological time it has contributed much to heating the plant earth internally!). 

Activity  - enter the numerical value of activity. 

Activity unit - choose Bq or Ci. Despite the SI unit being dominant around the world, the Curie is still often used when describing HASS sources in industrial irradiation (it is often easier to state 10 kCi Co-60 as apposed to 370 TBq, especially since such sources are still supplied in multiples of curies).

Activity multiplier - apply a multiplier to the activity (e.g. micro, milli, base, mega, giga etc). 

Output power units - choose from W, mW or kW. 

Additional power scenarios - the default selection is none - this gives a watt is a watt conversion which is idealistic. Alternatively choose from heat water, phone charging time or RTG electrical output. Each of these have submenus, some of which we will describe in the calculator use notes which follow below. 

Basic output - the basic output (no additional power scenarios) is obtained by clicking the calculate button. The output provide the following:

• The decay heat (W) for the selected radionuclide and activity.
• The approximate mass of radioactive material.
• How this energy can compared to that needed to power modern phone chargers or a 1kW electric bar fire. 

A note on half life. The calculator considers constant power, that is - the energy being produced is constant so that decay is not considered. However, when using the power scenarios (see below), the calculator will detail if half life actually matters in a particular given case. 

Phone charging time

You have a mobile phone with a battery capacity of 15 Wh. (The Wh can be calculated by multiplying the battery mAh rating with the voltage of the charger). You determine you have the following:

• 650 GBq Am-241 source.
• A suitable way of converting decay heat to electricity.
• A need to charge the phone by up to 25%.
• Your conversion is "RTG like"  - so an efficiency of perhaps 6 %.

Plug the numbers above into the calculator and see what you end up with!  Here are some highlights!

• 4.5g of Am-241 will be required (metal equivalent).
• The decay heat will be 0.0364 W (not a lot ...).
• To charge the phone as specified above, will take 4.5 days.
• The effect of half-life is negligible. 

So in theory this would work. But in practice, plugging your phone charger into the wall is going to be far simpler (and safer). 650 GBq Am-241 is a considerable alpha, beta and gamma source. At this activity the source might be combined with beryllium to form an AmBe neutron source (so you might have a neutron dose rate hazard and therefore considerable neutron shielding required). Just considering Am-241 on its own, it will yield an absorbed dose in air of 2413.45 µGy/h at 1m (so not trivial). Up close (say 10cm) the dose rate increases to 241345 µGy/h (photons) - therefore you are going to need some photon shielding in any case. 

What to investigate further?

How about trying out the Ionactive specific activity calculator? Half-life and specific activity are very much related, so this linked calculator is complementary.