dosimetry: absorbed dose and equivalent dose

This week, we’ve looked at calculating radiation doses.  The absorbed dose D, measured in Grays (Gy), takes into account the energy E absorbed and the mass m of the absorbing tissue.

D~=~E/m

The higher the energy, the greater the absorbed dose.  If you are wondering why the absorbing mass is important, consider the different masses of tissue involved in a dental x-ray and a chest x-ray….

We also learned about equivalent dose in Sieverts (Sv). The equivalent dose H gives an indication of the potential for biological harm by considering the absorbed dose D and a weighting factor W_R.

H~=~DW_R

Different types of radiation have different weighting factors, e.g.

type of radiationweighting factor
gamma1
x-ray1
beta1
alpha20

The more damaging forms of radiation have a larger weighting factor.

Absorbed dose and equivalent dose are usually expressed in smaller units; μGy, mGy, μSv, mSv.

In the UK, the Government has set an effective equivalent dose of 1mSv per year for members of the public.  This limit can be increased to 20mSv for people who work in the nuclear industry, certain medical occupations (such as radiographers) and airline pilots – all of whom will exceed the public limit in the course of their job.

This occupational increase for some individuals can be justified on the grounds that workers are not as vulnerable to the effects of radiation exposure since they are neither children (high rate of cell division so more chance of dna damage being copied) or elderly (reduced ability to repair damage).  In many cases, these workers will also be screened on a regular basis by occupational health staff at their place of work.

Here is a poster from the excellent xkcd site that explores examples of the different levels of equivalent dose.

Click on the picture for a larger version.

source: XKCD

Notice that the scale changes as you move through the poster from blue to green to red.

The dosimetry topic is comprehensively covered at BBC Bitesize.

geiger-müller tube

We’ve examined the operation of a Geiger-Müller counter as part of the radiation topic.

image by Theresa Knott

The Geiger-Müller (GM) counter is used to detect ionising radiation such as alpha and beta particles or gamma rays.  The radiation enters through a very thin window at one end of the tube.  This window is usually made of mica.

Mica flakes.  Photo by Rpervinking

Mica is a mineral that forms in layers called sheets.  These sheets can be split apart into very thin layers, so thin that even an alpha particle can pass through it (remember that alpha particles can be stopped by something as thin as your skin or a sheet of paper).  The mica window prevents the argon inside the tube from escaping and also stops air from getting into the tube.

When radiation enters the tube and collides with an argon atom, an electron may be knocked off the atom – we call this process ionisation.  When ionisation occurs, a positively-charged argon ion and a negatively-charged electron are produced.  The argon ion is attracted to the outside wall of the tube, which is connected to the negative terminal of the power supply, while the electron is attracted to the central electrode, which is kept at a high positive voltage – typically 500V.

A small pulse of current is produced each time an electron reaches the central electrode.  These pulses can be counted by an electronic circuit and a displayed on a 7-segment display.  Sometimes a small speaker is added to the system to produce a click for each pulse.  On its own, the GM tube cannot tell the difference between alpha, beta and gamma radiation.  We need to place different materials (e.g. paper, aluminium, lead) in front of the mica window to discover which type of radiation is responsible for the reading.

Here is a short video demonstrating the use of a Geiger-Müller tube.

 

x-rays

X-rays are a form of electromagnetic radiation.  They have a much higher frequency than visible light or ultraviolet.  The diagram below, taken from Wikipedia, shows where x-rays sit in the electromagnetic spectrum.

image by Materialscientist

Wilhelm Röntgen discovered x-rays and the image below is the first x-ray image ever taken.  It shows Mrs. Röntgen’s hand and wedding ring.  The x-ray source used by Röntgen was quite weak, so his wife had to hold her hand still for about 15 minutes to expose the film.  Can you imagine waiting that long nowadays?

This was the first time anyone had seen inside a human body without cutting it open.  Poor Mrs. Röntgen was so alarmed by the sight of the image made by her husband that she cried out “I have seen my death!” Or, since she was in Germany, it might have been

Ich habe meinen Tod gesehen!

that she actually said.

Röntgen continued to work on x-rays until he was able to produce better images. The x-ray below was taken about a year after the first x-ray and you can see the improvements in quality.

Notice that these early x-rays are the opposite of what we would expect to see today. They show dark bones on a lighter background while we are used to seeing white bones on a dark background, such as the x-ray shown below.  The difference is due to the processing the film has received after being exposed to x-rays.

In hospitals, x-rays expose a film which is then developed and viewed with bright light.  X-rays are able to travel through soft body tissue and the film behind receives a large exposure.  The x-rays darken the film. More dense structures such as bone, metal fillings in teeth, artificial hip/knee joints, etc. block the path of x-rays and prevent them from reaching the film.  Unexposed regions of the film remain light in colour.

Röntgen’s x-ray films would have involved additional processing steps.  The exposed films were developed and used to create a positive.  In creating a positive, light areas become dark and dark areas become light.  So the light and dark areas in Röntgen’s x-rays are the opposite of what we see today.  Our modern method makes it easier to detect issues in the bones as they are the lighter areas.

Röntgen was awarded the first ever Nobel Prize for Physics in 1901 for his pioneering work in this field of physics.

 

I have attached a recording of a short BBC radio programme about the first x-ray and what people in the Victorian era thought of these new images.  Click on the player at the end of this post or listen to it in iTunes.

total internal reflection

Earlier this week, we used semi-circular perspex blocks to investigate total internal reflection.

I’ve put together a short video showing total internal reflection in a semicircular block and a perspex model of an optical fibre.

total internal reflection from mr mackenzie on Vimeo.

There are some nice ray diagrams explaining total internal reflection on BBC Bitesize.

Cyberphysics has some examples of how optical fibers are used and the youtube video below shows how they can be used by doctors to see inside a patient’s body.

using linest to obtain a gradient and uncertainty

The period (T) of a simple pendulum can be calculated using

T=2 pi sqrt{l/g}

where l is the pendulum length and g is the gravitational field strength.

Using a single value of length and period, we can determine the acceleration due to gravity.  However, it would be better experimental practise to vary the length of the pendulum and plot a graph of T^2 against length, determining g from the gradient of the line of best fit.

 

You’re going to spend the next few periods analysing your simple pendulum data.  The attached pdf will walk you through the steps.  It would be better if you used your own results but I’ve put some sample data on the first page if you’ve forgotten to bring yours.

If you are using your chromebook, there may be subtle differences from the Excel instructions I have provided.  Let me know if anything doesn’t work and I’ll try to help.

Note that if you are using your own data, there will be no random uncertainty as measurements were not repeated.