FHSST Physics/Atomic Nucleus/Radioactivity

Radioactivity

As was said before, the nucleus experiences the intense struggle between the electric repulsion of protons and nuclear attraction of the nucleons to each other. It therefore should not be surprising that there are many nuclei that are unstable. They can spontaneously (i.e. without an external push) break in pieces. When the fragments reach the distances where the short range nuclear attraction disappears, they fiercely push each other away by the electric forces. Thus accelerated, they move in different directions like small bullets making destruction on their way. This is an example of nuclear radioactivity but there are several other varieties of radioactive decay.

Discovery of radioactivity

Nuclear radioactivity was discovered by Antoine Henri Becquerel in 1896. Following Wilhelm Roentgen who discovered the X-rays, Becquerel pursued his own investigations of these mysterious rays.

The material Becquerel chose to work with contained uranium. He found that the crystals containing uranium and exposed to sunlight, made images on photographic plates even wrapped in black paper. He mistakenly concluded that the sun's energy was being absorbed by the uranium which then emitted X-rays. The truth was revealed thanks to bad weather.katie

On the 26th and 27 February 1896 the skies over Paris were overcast and the uranium crystals Becquerel intended to expose to the sun were returned to a drawer and put over (by chance) the photographic plates. On the first of March, Becquerel developed the plates and to his surprise, found that the images on them were clear and strong. Therefore the uranium emitted radiation without an external source of energy such as the sun. This was the first observation of the nuclear radioactivity.

Later, Becquerel demonstrated that the uranium radiation was similar to the X-rays but, unlike them, could be deflected by a magnetic field and therefore must consist of charged particles. For his discovery of radioactivity, Becquerel was awarded the 1903 Nobel Prize for physics.

Nuclear alpha, beta, and gamma rays

Classical experiment that revealed complex content of the nuclear radiation, was done as follows. The radium crystals (another radioactive element) were put at the bottom of a narrow straight channel made in a thick piece of lead and open at one side. The lead absorbed everything except the particles moving along the channel. This device therefore produced a flux of particles moving in one direction like bullets from a machine gun. In front of the channel was a photoplate that could register the particles.

Without the magnetic field, the image on the plate was in the form of one single dot. When the device was immersed into a perpendicular magnetic field, the flux of particles was split in three fluxes, which was reflected by three dots on the photographic plate.

One of the three fluxes was straight, while two others were deflected in opposite directions. This showed that the initial flux contained positive, negative, and neutral particles. They were named respectively the $\alpha$ $\beta$, and $\gamma$ particles.

The $\alpha$-rays were found to be the ${}^{4}$He nuclei, two protons and two neutrons bound together. They have weak penetrating ability, a few centimeters of air or a few sheets of paper can effectively block them. The $\beta$-rays proved to be electrons. They have a greater penetrating power than the $\alpha$-particles and can penetrate 3mm of aluminum. The $\gamma$-rays are not deflected because they are high energy photons. They have the same nature as the radio waves, visible light, and the X-rays, but have much shorter wavelength and therefore are much more energetic. Among the three, the $\gamma$-rays have the greatest penetrating power being able to pass through several centimeters of lead and still be detected on the other side.

Danger of the ionizing radiation

The $\alpha$, $\beta$, and $\gamma$ particles moving through matter, collide with atoms and knock out electrons from them, i.e. make positive ions out of the atoms. This is why these rays are called ionizing radiation.

Apart from ionizing the atoms, this radiation destroys molecules. For humans and all other organisms, this is the most dangerous feature of the radiation. Imagine thousands of tiny tiny bullets passing through your body and making destruction on their way. Although people do not feel any pain when exposed to nuclear radiation, it harms the cells of the body and thus can make people sick or even kill them. Illness can strike people years after their exposure to nuclear radiation. For example, the ionizing particles can randomly modify the DNA (long organic molecules that store all the information on how a particular cell should function in the body). As a result, some cells with wrong DNA may become cancer cells.

Fortunately, our body is able to repair some damages caused by radiation. Indeed, we are constantly bombarded by the radiation coming from the outer space as well as from the inner parts of our own planet and still survive. However, if the number of damages becomes too large, the body will not cope with them anymore.

There are established norms and acceptable limits for the radiation that are considered safe for human body. If you are going to work in contact with radioactive materials or near them, make sure that the exposure dose is monitored and the limits are adhered to.

You should understand that no costume can protect you from $\gamma$-rays! Only a thick wall of concrete or metal can stop them. The special costumes and masks that people wear when handling radioactive materials, protect them not from the rays but from contamination with those materials. Imagine if few specks of radioactive dirt stain your everyday clothes or if you inhale radioactive atoms. They will remain with you all the time and will shoot the bullets at you even when you are sleeping.

In many cases, a very effective way of protecting yourself from the radiation is to keep a certain distance away. Radiation from nuclear sources is distributed equally in all directions. Therefore the number $n$ of dangerous particles passing every second through a unit area (say $1cm^{2}$) is the total number $N$ of particles emitted during 1 second, divided by the surface of a sphere

$n={\frac {N}{4\pi r^{2}}}\$,

where $r$ is the distance at which we make the observation. From this simple formula, it is seen that the radiation intensity falls down with increasing distance quadratically. In other words, if you increase the distance by a factor of 2, your exposure to the radiation will be decreased by a factor of 4.

Decay law

Unstable nuclei decay spontaneously. A given nucleus can decay next moment, next day or even next century. Nobody can predict when it is going to happen. Despite this seemingly chaotic and unscientific situation, there is a strict order in all this.

Atomic nuclei, being microscopic objects, are ruled by quantum probabilistic laws. Although we cannot predict the exact moment of its decay, we can calculate the probability that a nucleus will decay within this or that time interval. Nuclei decay because of their internal dynamics and not because they become old or somehow rotten.

To illustrate this, let us imagine that yesterday morning we found that a certain nucleus was going to decay within 24 hours with the probability of 50%. However, this morning we found that it is still alive. This fact does not mean that the decay probability for another 24 hours increased. Not at all! It remains the same, 50%, because the nucleus remains the same, nothing wrong happened to it. This can go on and on for centuries.

Actually, we never deal with individual nuclei but rather with huge numbers of identical nuclei. For such collections (ensembles) of quantum objects, the probabilistic laws become statistical laws. Let us assume that in the above example we had 1 million identical nuclei instead of only one. Then by this morning only half of these nuclei would survive because the decay probability for 24 hours was 50%. Among the remaining 500000 nuclei, 250000 will decay by tomorrow morning, then after another 24 hours only 125000 will remain and so on.

The number of unstable nuclei that are still alive continuously decreases with time according to the curve shown in Fig. 15.2

Figure: 15.2 The time T1/2 during which one half of the initial amount of unstable particles decay, is called their half-life time.

If initially, at time $t=0$, their number is $N_{0}$, then after certain time interval $T_{1/2}$ only half of these nuclei will remain, namely, ${\frac {1}{2}}N_{0}$. Another one half of the remaining half will decay during another such interval. So, after the time $2T_{1/2}$, we will have only one quarter of the initial amount, and so on. The time interval $T_{1/2}$, during which one half of unstable nuclei decay, is called their half-life time. It is specific for each unstable nucleus and vary from a fraction of a second to thousands and millions of years. A few examples of such lifetimes are given in Table 15.2

Table 15.2: Half-life times of several unstable isotopes. Half-life times of several unstable isotopes.

isotope	T1/2	decay mode
${}_{84}^{214}$Po	$1.64\times 10^{-4}$ s	$\alpha ,\gamma$
${}_{36}^{89}$ Kr	3.16 min	$\beta ^{-},\gamma$
${}_{86}^{222}$ Rn	3.83 days	$\alpha ,\gamma$
${}_{38}^{90}$Sr	28.5 years	$\beta _{}^{-}$
${}_{88}^{226}$ Ra	$1.6\times 10^{3}$	$\alpha ,\gamma$
${}_{6}^{14}$C	$5.73\times 10^{3}$	$\beta _{}^{-}$
${}_{92}^{238}$U	$4.47\times 10^{9}$	$\alpha ,\gamma$
${}_{49}^{115}$In	$4.41\times 10^{14}$	$\beta _{}^{-}$

Radioactive dating

Examining the amounts of the decay products makes possible radioactive dating. The most famous is the Carbon dating, a variety of radioactive dating which is applicable only to matter which was once living and presumed to be in equilibrium with the atmosphere, taking in carbon dioxide from the air for photosynthesis.

Cosmic ray protons blast nuclei in the upper atmosphere, producing neutrons which in turn bombard nitrogen, the major constituent of the atmosphere. This neutron bombardment produces the radioactive isotope ${}_{6}^{14}$C. The radioactive carbon-14 combines with oxygen to form carbon dioxide and is incorporated into the cycle of living things.

The isotope ${}_{6}^{14}$ decays (see Table 15.2) inside living bodies but is replenished from the air and food. Therefore, while an organism is alive, the concentration of this isotope in the body remains constant. After death, the replenishment from the breath and food stops, but the isotopes that are in the dead body continue to decay. As a result the concentration of ${}_{6}^{14}$C in it gradually decreases according to the curve shown in Fig. 15.2. The time $t=0$ on this Figure corresponds to the moment of death, and $N_{0}$ is the equilibrium concentration of ${}_{6}^{14}$C in living organisms.

Therefore, by measuring the radioactive emissions from once-living matter and comparing its activity with the equilibrium level of emissions from things living today, an estimation of the time elapsed can be made. For example, if the rate of the radioactive emissions from a piece of wood, caused by the decay of ${}_{6}^{14}$C, is one-half lower than from living trees, then we can conclude that we are at the point $t=T_{1/2}$ on the curve 15.2, i.e. it is elapsed exactly one half-life-time period. According to the Table 15.2, this means that the tree, from which this piece of wood was made, was cut approximately 5730 years ago.

This is how physicists help archaeologists to assign dates to various organic materials.