Timed Solid Disposal

t = -(T_½/0.693) * ln(D.L./(Initial Activity/mass))

If you know the activity and mass of a container of waste, you can use this equation to find out how long to hold the container for decay. The initial activity should be given in MBq and the mass in kg, however, you could also enter the activity in kBq and the mass in g and get the correct result. If you do not know how much activity is in the container you should hold it for a minimum of 10 half-lives.

In Canada the Disposal Limits (DL) for radioactive waste are provided by the Canadian Nuclear Safety Commission (CNSC). The disposal limits for the following 22 commonly used radioisotopes have been provided by the CNSC and are available in this calculator; however, you should always refer to your license or contact your radiation safety officer for the solid waste disposal limit of the isotope you are working with.

Sb-124, Br-82, C-14, Cr-51, Co-57, Co-58, Co-60, F-18, Ga-67, H-3, In-111, I-123, I-125, I-131, Fe-59, P-32, P-33, Ra-226, Na-22, Sr-85, Tc-99m, Tl-201

If the disposal limit for your isotope is not included in this calculator, or is different from the value displayed, you can still use the equation by entering the value (in MBq/kg or kBq/g) in the Disposal Limits: Solid textbox.

Radioactive waste exceeding the prescribed limits is typically held for decay by the licensee if the isotope has a half-life of less than 90 days, and is sent to an approved radioactive waste storage facility for isotopes with half-life greater than 90 days. Check your license conditions or contact your radiation safety officer if you are unsure.

To use the equation:
The information required by the equation is the initial activity (N_o), the mass (m), the half-life of the isotope (T_½), and its Solid Disposal Limit (DL).

1. Select the isotope from the list at the top of the page; the isotope's half-life appears in the Half-life textbox and Solid Disposal Limit appears in the Solid (MBq/kg) textbox in the section below the equations.
2. Enter the initial activity in MBq.
3. Enter the mass in kg.
4. Click the Calculate button and the decay time is displayed. The time unit will be the same as the half-life unit. The value is rounded to the nearest whole time unit.

An example:
Your waste container has 25.25 MBq of P-32 and weighs 4.5 kg. How long until it can be disposed of?

1. Select Phosphorus 32 from the isotope list. 14.262 and d show up in the Half-life and Half-life time unit textboxes, while 0.37 appears in the Solid (MBq/kg) textbox in the section below the equations.
2. Enter 25.25 in the Initial activity (N_o) textbox.
3. Enter 4.5 in the mass (kg) textbox.
4. Click the Calculate button and the answer 56 d is received.
5. You can then use the time calculator to find out the date 56 days from now.

Advanced:
If your isotope is not on the list, you can still use the equation if you know the half-life and the solid waste disposal limit of your isotope. First manually enter the half-life in the Half-life textbox at the top of the page. You can get half-life values here. Enter the solid waste disposal limit in the Solid (MBq/kg) textbox in the section below the equations. Then use the equation as described above.