**Full credit to**

**http://nuclearcrimes.org/conversions.php**

**RADIOACTIVE-'ACTIVITY'**

To determine how radioactive something is:

A ^{*} = | 0.693 mN _{A} |

| T_{1/2}AF_{t} |

m = mass of sample

A = atomic weight of radionuclide (easy: it's the number of the nuclide, like 89 for strontium-89)

T

_{1/2}= half-life of radionuclide (in any unit of time)

F

_{t}= conversion from one unit of time to the desired unit of time

N

_{A}= constant called Avogadro's number, or 6.022 x 10

^{23}atoms/mole

**Does this formula really work?**

Let's try it on radium. We know that 1 curie represents the radioactivity of one gram of pure Radium-226 and we also know that 1 curie pumps out 3.700 x 10

^{10}disintegrations per second.

So, to prove that 1 gram of radium pumps out 37 trillion disintegrations per second, let's assign the variables for radium. Lets assign a mass of 1 (gram). We know radium's half-life is about 1,603 years and its atomic weight is 226.0254 (radium 226). For F

_{t }we want to convert from years to seconds, or 31,536,000 seconds per year.

A ^{*} = | (0.693) (1 gram) (6.022 x 10 ^{23} atoms/mole) | = 3.65E10, or 3.65 x 10^{10 }disintegrations per second |

| (1603 years)(226.0254 grams/mole) (525600 minutes/year)(60 seconds/minute) |

**Example. If 1 microgram of strontium-89 (which has a 50.6 day half-life) was deposited today in 1 meter by 1 meter area of a rice patty near Tokyo, what is its present activity?**

A ^{*} = | (0.693) (0.00001 grams) (6.022 x 10 ^{23} atoms/mole) | = 6.43 x 10^{11 }disintegrations per minute |

| (50.6 days)(89 grams/mole) (1440 minutes/day) |

**Example. If plutonium-238 depositions from Fukushima caused Namie soils to be 4 becquerels per square meter, what is the activity level?**

First 4 becquerels (of pu238) is the same as 108 picocuries (of pu238). Second, one gram of pu238 is 17.44 curies, or (17.44 x 1 trillion) picocuries. So, the 4 becquerels per square meter represents 108/(17.44 x 1 trillion) = 6.3 x 10

^{-12}grams.

A ^{*} = | (0.693) (6.3 x 10 ^{-12} grams) (6.022 x 10 ^{23} atoms/mole) | = 238.8 disintegrations per minute |

| (88 years)(238 grams/mole) (525600 minutes/year) |

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