## Curie to Becquerel – Conversion

The original unit for measuring the amount of radioactivity was the **curie** (symbol Ci), which is a non-SI **unit of radioactivity** defined in 1910. A** curie** was originally named in honour of **Pierre Curie**, but was considered at least by some to be in honour of Marie Curie as well. A curie was originally defined as equivalent to the number of disintegrations that **one gram of radium-226** will undergo in **one second**. Currently, a curie is defined as **1Ci = 3.7 x 10 ^{10} disintegrations per second**. Therefore:

**1Ci = 3.7 x 10 ^{10} Bq = 37 GBq**

The SI unit for measuring the amount of radioactivity is the **becquerel** (symbol** Bq**). The **becquerel** is named in honour of Henri Becquerel, a French physicist who discovered radioactivity in 1896. **One becquerel** (1Bq) is equal to **1 disintegration per second**.

## Curie to Becquerel – Problem with Solution

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

**Calculate:**

- The number of iodine-131 atoms initially present.
- The activity of the iodine-131 in curies.
- The number of iodine-131 atoms that will remain in 50 days.
- The time it will take for the activity to reach 0.1 mCi.

**Solution:**

- The number of atoms of iodine-131 can be determined using isotopic mass as below.

**N**_{I-131}** = m**_{I-131}** . N**_{A}** / M**_{I-131}

**N**_{I-131 }**= (1 μg) x (6.02×10**^{23}** nuclei/mol) / (130.91 g/mol)**

**N**_{I-131}** = 4.6 x 10**^{15}** nuclei**

- The activity of the iodine-131 in curies can be determined using its
**decay constant**:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_{50d}) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2^{10} = 1024) is widely used to define residual activity.

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