Potassium – Natural Body Radiation
We don’t directly feel nuclear radiation, but it is present all around us — and even within us! Potassium ions are vital for the functioning of all living cells, vegetables and fruits are good potassium sources. So if you are eating a healthy diet, you probably carry around 140 g of potassium. While most of the potassium atoms are stable, 0.012% is the active 40K isotope with a half-life of 1.24 billion years.
How many radio active potassium ions are in your body?
The avogadro constant describes how many atomes (or molecules) there are per mole of the substance. The constant is built-in to Calcumber as _NA.
The molecular weight of 40K is 40 g/mol.
Potassium in body: m_K = 140 g;
Of which radio active: m = m_K / 100 * 0.012 ➔ 0.0168 g
Number of atoms: n = m / (40 g/mol) * _NA ➔ 2.529e20
How many of decays pers second does this amount produce?
Decay rate (Activity): A = ln(2) * n / t_h ➔ 1.359e10 1/year
Calcumber automatically uses the input units, which is year. To get the result per second:
use s ➔ 427 1/s
There is quite some noise in us, isn’t there?
What energy dose is deposited in a 70 kg person?
Assumption: 1.3 MeV energy is deposited within our body per decay.
Decay energy: Q = 1.3 MeV;
Dose in a year: A * Q * 1 year / (70 kg) ➔ 4.0127e-5 Gy
use uGy ➔ 40.127 uGy
Is there a link between the high flammability and the radioactivity of potassium?
No, the reaction with oxygen is a chemical reaction while the other is a nuclear reaction.
Chemical: the electon arrangement of potassium and oxygen is changed to a lower level, emitting energy in the range of eV.
Nuclear: a neutron decays to an electron and a proton. As a result, the atom has one proton more and becomes 40Ca. The emitted energy is in the range of MeV, 1000 times higher compared to a chemical reaction. However the reaction rate of about 400 1/s is moderate, that’s why we don’t all spontaneously catch fire!
What is the average annual radiation dose we are exposed to (not only 40K)?
Interesting information you find on a page on Radiation Doses of the government of Canada. The dosis varies, it is something between 1 mSv and 12 mSv of natural dosis in an extreme case! An average is about 2 mSv.
Sievert is the radiation dose weighted by health impact. For the beta radiation of potassium, the weighting factor is 1. So the 40 µGy from the potassium in our body, the equivalent dose is 40 µSv, which is 2% of the average annual dose.
Calculation in Calcumber
Open this example in Calcumber Web App.
More on Potassium
Potassium in its metallic form is so soft, that you can cut it with a knife!
It reacts instantly with oxygen and water, often bursting into flames. It must therefore be stored under oil or vacuum.
The name comes from potash – the ash of plants from which it is first isolated.
Deriving the Activity Formula
Exponential decay with half-life t_h:
$$n(t) = n_0 2^{- \frac {t} {t_h}} = n_0 e^{ – { ln 2 } \frac {t} {t_h}} $$
Derived by time:
$$\dot{n}(t) = – n_0 \frac { \mathrm{ln 2} } { t_h } e^{ – \frac { \mathrm{ln 2} } { t_h } t} $$
$$\dot{n}(0) = – \frac {n_0} { t_h } \mathrm { ln 2 } $$
Activity:
$$A = – \dot {n}(0) = \frac {n_0} {t_h} ln 2$$
Links
Wikipedia: Potassium
Government of Canada: Radiation Doses
A great intro, sources of doses and numbers for yearly dose
Wikipedia: Sievert
About the equivalent dosis Sievert and how it relates to the absorbed dose Grey.
UK Government: Ionising radiation – dose comparisions
A great table of doeses for different exposures
