Make an order-of-magnitude estimate of the amount of radon- 222 gas, measured in curies, found i

Make an order-of-magnitude estimate of the amount of radon-...

Key Concepts

Radioactive Decay

This concept refers to the process by which an unstable atomic nucleus loses energy by emitting radiation. It is fundamental in understanding how radioactive isotopes, such as radon-222, decrease in number over time. The decay process is probabilistic and described using exponential functions, which are used to predict the remaining amount of the substance at any given time after its production.

Half-Life

Half-life is the time required for half of the radioactive atoms in a sample to decay. It is a critical parameter in nuclear physics and radiological protection because it allows one to calculate the decay constant, which is used in further calculations determining how quickly radioactivity diminishes. In practical scenarios, such as assessing radon exposure in lungs, the known half-life aids in estimating the equilibrium activity in the body.

Radioactivity Units

Radioactivity is quantified using units such as the curie, which measures the rate of decay of radioactive material. One curie represents a specific number of disintegrations per second. Understanding these units is essential when converting between the activity present in a substance and the biological or environmental effects of that activity.

Alpha Particle Emission

Alpha decay is a type of radioactive decay characterized by the emission of alpha particles, which are helium nuclei composed of two protons and two neutrons. These particles have discrete energy levels, and by calculating their energy, one can determine the dose delivered upon interaction with matter. This information helps in assessing health risks linked to radon exposure, particularly due to the ionizing radiation from alpha particles.

Radiation Dosimetry

This field involves the calculation and assessment of the radiation dose absorbed by human tissue. In the context of radon, dosimetry connects the energy output of alpha particles to the rem (roentgen equivalent man) unit, which is used to estimate the biological effect of the radiation. It is crucial for estimating exposure levels, as demonstrated by linking the energy of emitted alpha particles to an annual dose of 0.1 rem.

Order-of-Magnitude Estimation

Order-of-magnitude estimation is a problem-solving technique that involves approximating a calculation to the nearest power of ten. This approach simplifies complex physical problems, such as estimating the amount of radon in the lungs, by focusing on the scale of the quantities involved rather than precise values. It is particularly useful when dealing with uncertainties in biological parameters and environmental radiation.

Transcript

00:01 So in this question we are looking at the decay of radon 2222 and we want to find out how many gas there are in the lung given a particular dose rate that we see over here which is 0 .1 rem per year.

00:20 So we want to convert this 0 .1 rem first.

00:25 So 0 .1 r em actually is equals to 0 .01 cverts.

00:40 Right, and to convert severs, cvors is actually equals to dose times the quality factor.

00:47 Right, so quality factor for alpha particles is 15, right specifically for alpha particles.

00:59 So our dose, we can calculate our dose per year to be 0 .01 divided by 15 juice per kilogram.

01:15 Now we want to find, okay, so let me just evaluate this, this will be 0 .7 .5 juice per kg.

01:33 Now the average mass of average person would be estimated to be around 70 kg.

01:43 If we estimate the mass to be around 70 kg, then the total energy absorbed.

01:50 Energy absorbed, goes to dose multiplied by 70 kg.

01:59 And then that would be probably around 0 .0, 469 juice per year, right? this is all the dose per year since you are starting with 0 .1, i am.

02:18 Now we're going to find the dose or the energy absorbed.

02:21 Energy absorbed per second.

02:27 And to do that, we can just simply divide the time thing by the number of seconds in a year.

02:36 And there will be 365 days, 24 hours, for each day, 3 ,600 seconds per day.

02:45 And since we are dealing with really really small numbers, so it will be good if we can convert it into electron folds.

02:59 Electron volts would be to convert it into electron volts we simply divided into by 1 .60 times 10 to power of minus 19 and this will give us electron volts which is very convenient since we are dealing with very small numbers and put it into our calculator we should get 930 mev now this is the energy absorbed per second okay so now moving on moving on to the actual decay itself.

03:37 Now the reason we are looking at the decay itself is to find out what is the energy of the alpha particle.

03:48 Right? so for an alpha particle decay, we know that the alpha particle is a helium nuclei and so two protons are lost.

04:00 And having lost two protons, the resulting proton is 84 and so the element of our interest of our daughter nucleate would be polo with a nuclear number of 218, right? because 2 -2 -2 subtracted by 4, you get 218.

04:20 To get the energy of the helium, we need to take the mass of the product and the mass of the paramuclide and find out what's the difference...

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