Quote of the Day

No one ever won a medal for an on-time failure.

— Frank McDonald, NASA Chief Scientist

## Introduction

I am not a cat person – the only time that cats come up in my family is in regards to Schrodinger's cat (Figure 1). However, I just came across an interesting web page by the Oak Ridge Associated Universities that discusses cat litter and the fact that it is slightly radioactive. Some cat litter is slightly radioactive because the contain bentonite clay, which contains small amounts of radioactive uranium (^{238}U), thorium (^{232}U), and potassium (^{40}K). I find this web page interesting because it includes measured radiation data and an estimate of the heavy metals (uranium and thorium) that are contained in cat litter.

I thought it would be interesting going into the details of the associated calculations. Here are the key numbers presented on the webpage:

- 4 billion pounds of clay-based cat litter per year are used (reasonable number, but no source given).
- 50,000 pounds of uranium are in this cat litter.
- 120,000 pounds of thorium are in this cat litter.

To confirm the estimates for the amount radioactive elements, I will use the following radiation measurements made by the web page author:

- 4 picoCuries (pCi) of
^{238}U radiation per gram of cat litter. - 3 pCi of
^{232}Th radiation per gram of cat litter. - 8 pCi of
^{40}K radiation per gram of cat litter.

## Background

### Amount of Clay-Based Cat Litter Manufactured Per Year

The following quote from this web page tells us how much clay-based cat litter is produced in the US every year, which I will need in the calculations to follow.

Clay-based cat litter must be mined. The United States Geological Society estimates that 85 percent of the 2.54 million tons of clay used in this country every year is used for absorption of pet waste, with cat litter being the dominant. There are about 20 companies operating such mines in 10 states.

### Basics of Radioactivity Calculations

There are numerous places to learn about how to do calculations involving radioactive materials. On this blog, I have examples on the following posts:

- Granite Self-Heating Math
- Nuclear Battery Math
- Radioactive Banana Math
- How Much Radioactive Material is in a Smoke Alarm?

## Analysis

### Approach

Since I have radiation measurements for each element for a given mass (one gram) of cat litter, I can estimate the amount of uranium, thorium, and potassium in a gram of litter if I know the amount of radiation produced per gram by uranium, thorium, and potassium. Once I know the amount of radioactive element per gram of litter, I can compute the amount of heavy metals disposed of in cat litter per year using the total mass of clay-based cat litter produced per year.

### Basic Radioactivity Math

Figure 2 shows how I computed the number of decays per second for each gram of ^{238}U, ^{232}Th, and ^{40}K using the half-life formula. I am assuming that ^{238}U is the dominant source of radiation from uranium, which has a number of radioactive isotopes (e.g. ^{235}U). I demonstrate that this assumption is correct in Appendix B.

I put an independent check on these figures in Appendix A.

### Mass of Uranium and Thorium Disposed Per Year

Figure 3 shows how I can take the radiation measurements from the reference article and compute the amount of uranium and thorium present in each year's cat litter production (clay-based only).

## Conclusion

I was able to confirm all the figures on the Oak Ridge Associated Universities web page. This is just more confirmation that radiation is all around us.

## Appendix A: Check Figures.

Figure 4 shows values for the radiation emission measured from bentonite clay that I found in a research paper.

To make for easier reading, I have extracted the radiation emission values into the following list.

- 1 ppm
^{238}U radiates at a rate of 12.4 Bq/kg. - 1 ppm
^{232}Th radiates at a rate of 4.06 Bq/kg. - 1% K (0.0119%
^{40}K) radiates at a rate of 313 Bq/kg.

In Figure 4, I take the radiation levels that I computed in Figure 2, performed some unit conversions, and I confirm agreement with Figure 5.

## Appendix B: Decay Contributions of Different Uranium Isotopes.

Figure 6 shows that ^{238}U generates 96% of the decay activity in natural uranium. For the rough analysis being performed in this post, I will assume all the radiation comes from ^{238}U.

Pingback: Radioactive Paper? | Math Encounters Blog

Fool. You forgot to carry the 2. Basic schoolboy error.

I think those degrees of radiation are too small to produce humans and pets hazards. Do you have any study about which type of radiation comes out of bentonite clay e.g. gamma, beta, or alpha radiations?

Best regards and wishes.

In my post, I discuss the particular isotopes of uranium, thorium, and potassium present. You can look up these isotopes on the Wikipedia, where you will find their particular emissions.

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