K11 Radioactivity

Fundamental observations of radioactivity

The French scientist Becquerel 1896 discovered that uranium and all its alloys emit enduringly and spontaneously rays, which perpetrate substances of all kinds. These rays blackened photographic plates and ionized air. The intensity of the radiation only depended on the quantity of uranium in an alloy and the chemical binding was unimportant. Hence the ability to radiate had to be a property of the uranium itself, that is, the uranium atom. Curie-Sklodowska discovered with several natural uranium ores (pitchblende of Johanngeorgenstadt in Saxony and of Joachimsthal in Bohemia) an ability to radiate, which was much in excess of their uranium content. She concluded from this boldly that both ores contained a new type of atom - a hitherto unknown element - which radiates more strongly than uranium. She succeeded indeed to separate the new element - radium - which radiates millions times more strongly than uranium. Since then, several other elements with similar properties have been discovered: Thorium, actinium, polonium. All these substances, which radiate like uranium and radium, are said to be radioactive. However, their behaviours differ greatly. While you observe with some elements a constant ability to radiate, one has also separated from pitchblende substances with a variable radiation; for some it vanished completely in the course of hours or days. There were also cases in which an initially very weak radioactivity increased substantially with time. All these phenomena, which in their variety were then confusing, are explained by the disintegration theory, developed by Rutherford and Soddy 1902.

Disintegration theory

This theory sets out from the concept that every atom of a radioactive element disintegrates earlier or later explosively, when either a helium atom (a-ray) or an electron (b-ray) is emitted at a high velocity. The remaining chief constituent of the atom has other physical and chemical properties than the initial atom, that is, it represents a new kind of atom, a new element. In the course of time, this atom converts as well by emission of a- or b-rays into a third element, etc., until an element without radioactive properties is formed.

Consider radium as a typical example: Its chemical and physical properties are equally well defined and known as those of any other (inactive) element. However, while the atoms of inactive elements are stable and, as far as we know, undergo changes, this is different for radium. A radium atom lives in the mean only about 2000 years, when it changes in an explosove manner and ceases to exist as a radium atom. The new atoms form altogether the radium-emanation - a radioactive gas - which continuously emits from radium preparations and on its part converts into a solid radio-element.

All radium would already have disappeared from Earth, if not ionium - its mother substance - were being formed newly all the time. But also ionium has ancestors; we can trace them back to the progenitor - uranium. We only know about uranium that is decomposes extremely slowly, millions times more slowly than radium, but we do not know its source, if it should exist.

|The table above shows the most important members of the uranium-radium sequence in genetic order. From uranium - here denoted by radium I - arises uranium X₁, then X₂, etc. We find at the end of the sequence lead, which lacks radioactive properties. The table states for each element the emitted kind of ray and the half-time, which measures the rate at which the element decomposes.

Apart from the uranium-radium sequence, there exist two other radio-active sequences - the actinium- and the thorium-sequence. Among the members of the thorium sequence, the mesothor, discovered by Hahn 1900, has a special role. Like radium, it is widely employed in medical treatment, but its life-time is short.

The different radioactive substances decompose at very different rates, some of them only in the course of billions of years, others in fractions of seconds. In no case, one has been able to influence the decomposition rate by external forces, neither by the highest attainable temperatures and pressures nor by cooling to the temperature of liquid oxygen or by intensive magnetic fields. Radioactivity is sited inside the innermost part of the atom - atomic nuclei - while physical and chemical forces can only affect atomic parts further outside - the electrons. The following comparison demonstrates the enormous forces involved in radioactive disintegration: The helium atom, which emits during the disintegration of its nucleus as an a-ray has a velocity of 20,000 km/sec; in order to achieve in helium gas the same average velocity of the atoms by a temperature increase, you require 6,500,000ºC. The temperature on the surface of the Sun is 6000 ºC.

Half-life time and disintegration constant

In order to follow an advancing decomposition of a radioactive substance, you let the emitted radiation enter a gold-leaf elctrometer (Fig. 429) and determine there the intensity of the generated ionization, since it is a measure for the number of rays emitting from the sample and thereby also a measure of radioactivity, that is, the number of atoms, disintegrating each second. If you examine a sample which contains only atoms of a single radioactive substance, you discover that the activity always drops in equal time intervals to the same fraction. For example, if a sample displays at an arbitrary instant an activity 100 and one hour later an activity 90, it will be after subsequent hours 0.9·90 = 0.81, 0.9·0.81 = 72.9, etc. In particular, if the activity drops within T hours to half its initial value, it will also continue to drop every T hours to half its value. Moreover, the selection of the starting instant is unimportant. The time, defined thereby, is called the decomposition time or half-life time.

As an example, consider the decrease in the activity of uranium X₁. If you add to a solution of uranium nitrate finely ground carbon and filter it after boiling it for a brief period, it has considerable activity. It occurs, because the uranium X₁ in the uranium- nitrate solution is readily absorbed by the animal charcoal. Let such an uranium X₁ sample be measured day after day and its activity be plotted against time (Fig. 527), where the initial activity has been set equal to 100. According to the curve A, the activity has sunk to half after 24 days, to a quarter after 48 days, to one eighth after 72 days, whence the half-time of uranium X₁ is 24 days.

A law of decrease, characterized by the activity and also thsaid to be exponential. Its mathematical form is n_t=n₀e^-lt, where n₀ and n_t are the numbers of initially and at time t disintegrating atoms and e is the basis of the natural logarithm (2.718..). The constant l is a characteristic quantity of the radioactive substance under consideration. It is related to the half-time T by the equation l ·T = ln 2 (ln denoting the natural logarithm to the base e) and represents the fraction of present atoms, decomposing in unit time. As a rule, the second is chosen as time unit; if, for example, l for uranium X₁ has the value 3.3·10^-7, this means: In every second decomposes exactly this fraction of the uranium X₁ atoms present. Hence, if the number of present atoms is N, the number of atoms decomposing per second is n=l ·N.

Since the number of disintegrating atoms is at each instant proportional to the number of the not yet decomposed atoms, you can also give the above equation the form N_t=N₀e^-lt, where now N₀ and N_t denote the numbers of the initially and yet present not decomposed atoms. Hence, for a uniform radioactive substance, the radiation and number of atoms decrease according to the same exponential law.

Radioactive equilibrium

It is not possible to pursue in a laboratory the conversion of uranium into its final product - lead -, because many of the elements in between have so long lives that the conversion products only accumulate into measurable quantities after thousands of years. In contrast, in uranium minerals, this conversion has progressed since times immemorial and an equilibrium state has been reached: Every element is present in such a quantity, that it receives by decomposition of the preceding element all the time as many new atoms as it loses by its own disintegration. Hence, if you were to count for a uranium mineral, which contains all the elements in the above table , how many atoms of each element disintegrate each second, you will find for each of them the same number. Denoting the number of atoms of the individual elements uranium I, uranium X₁, etc., which are present in a mineral, by N₁, N₂, N₃ ··· and the corresponding decomposition constants by l₁, l₂, l₃ ···, then l₁N₁, l₂N₂, l₃N₃ ··· atoms of these elements disintegrate each second, for l denotes the during one second decomposing fraction of the present atoms. At radioactive equilibrium, the same number of atoms of each element disintegrate per second, whence l₁N₁ = l₂N₂ = l₃N₃ = ···, that is, the present quantities N₁, N₂, N₃ ··· are interrelated inversely as the decompositions constants. In this manner, you find in a uranium mineral 0.000,000,34g radium per gram uranium. Hence, equally many atoms of 0.000,000,34 g radium disintegrate in the same time as from 1 g of uranium: On an average, 12,000 atoms per second.

If the radioactive equilibrium is disturbed by an external action, it will gradually again reinstall itself. For example, if you remove from the mineral half its radium, then only 6000 radium atoms per second will disintegrate, but, on the other hand, as before, 12000 arise from the mother substance. Hence the quantity of radium will increase, and indeed so long until subsequent formation and disintegration are again in equilibrium.

It is different in the case of the stable final member of the uranium-radium sequence - lead. The older (in millions of years) is a radioactive mineral, the more lead has accumulated in it. Eventually, it contains for every disintegrated uranium atom one lead atom. Like in the case of a sand-glass the amount of sand, accumulating down below, measure the time interval, while the clock is running, the amount of lead in a uranium mineral measures its age. A tenth gram of lead per one gram of uranium implies an age of 800 million years. The determination of the lead content of a radioactive mineral has become an important indicator for the determination of its geological age.

Formation of a radioactive substance from its mother substance

While uranium X₁, separated from uranium salt, gradually fades according to the curve A in Fig. 527, the disintegration of uranium I creates again fresh uranium X₁. If, as we assume, uranium X₁ was present ahead of the separation in an equilibrium amount, equally many uranium X₁ atoms were formed as disintegrated. The new formation of uranium X₁ from the uranium continues naturally also after the separation in the same manner as before. Hence, if the curve A shows that in one day 3% of the present amount of uranium X₁ disintegrates, the same amount of uranium X₁.must be formed newly in the uranium salt. If the separated uranium X₁ has halved after 24 days, also exactly half of the equilibrium amount turns up after this time in the uranium salt. You can readily convince yourself of this by separating 24 days after the first separation again turanium X₁. You discover then an activity which is half as large as that at the first separation.

The curve B in Fig. 527 demonstrates the law for the reproduction of uranium X₁ in a uranium salt. The curve B complements the curve A, that is, the sum of the activity of the separated and afterwards formed uranium X₁ and the sum of the two quantities have at all times the same value. You should read off the graph the two values at any time, to discover that the sum is 100. After about 6 months, the separated uranium X₁ has vanished completely, while you find in the uranium salt the equilibrium amount of uranium X₁.

This law, which has been explained by means of the example of uranium-uranium X₁ applies to all radioactive substances, whenever the mother substance has a long life compared with its subsequent substance. If this assumption does not apply, the circumstances are more difficult to survey.

Different kinds of rays of radioactive substances

Our experiences with cathode rays suggest that we should submit the radiation of a radioactive sample to a magnetic field (Fig. 528): The radioactive sample R is in a small box P, which is made out of lead and lets the rays emit upwards through a narrow slot. The escaping bundle of rays passes through a magnetic field, the line of force runs perpendicularly to the plane of the drawing (South pole in front, North pole at the back) and is decomposed as follows: One part - the a-radiation - is deflected in the same sense as positively charged particles (canal-rays), the second part - the b-radiation - is considerably more strongly deflected in the opposite direction., the third part - the g-radiation is not influenced by the magnetic field, that is, these rays do not have an electric charge.

The main properties of these three kinds of rays are:
1. The a-rays are with about 1/20 the velocity of light are helium nuclei. They carry a positive charge which is exactly twice as large as that of an electron. They can pass linearly through several centimetres of a thin metal foil or also air at atmospheric pressure. This distance is called radius of influence and is a characteristic quantity for each radioactive element. Among the elements of the uranium-radium sequence, the a-rays of radium C have the largest radius of influence of 6.97 cm. Uranium I with 2.67 cm has the smallest such radius. On their way through air or other gases, the a-rays generate extraordinarily many ions.
2. The b-rays have the same nature as cathode rays, that is, they consist of electrons. While their deflection in a magnetic field is considerably larger than that of the a-rays, it is very small in comparison with cathode rays, This is explained by their very large velocity which is almost that of light. You cannot generate so fast rays in discharge tubes; tensions of many millions of Volt would be required. While all the a-rays of a homogenous radioactive substance are emitted at the same velocity, this does not apply to b-rays, We find here rays with different velocities; this is indicated in Fig. 528 by the different deflections of the rays. The large velocity of the b-rays also is reflected in their characteristic ability to pass through all kinds of solids; an 1 mm thick aluminium sheet still lets pass an appreciable amount of b-rays. Among those of radium, there are rays which have the velocity of light.
3. The g-rays are emitted simultaneously with the b-rays. They are electro-magnetic oscillations like X-rays, but with much shorter wave lengths, whence their penetration ability is enormous. Layers of lead, many centimetres thick, are required to absorb them completely.

Proof of the helium nature of a-rays

It was very important for an explanation of radioactive phenomena and the development of atomic theory to study the nature of a-rays. This difficult question was resolved in the first place by the British scientist Rutherford. At first, the methods employed were the same which have been used during the study of the nature of cathode rays: Deflection measurements in magnetic and electric fields. These experiments yielded the ratio of charge to mass of 4820 electro-magnetic units, that is, exactly half that of hydrogen atoms. The deflections occurred in the sense of a positive charge. This suggested that the charge of an a-particle is twice as large, the mass four times as large as that of a positive hydrogen ion. Thereby the a-particle is characterized as a helium nucleus.

In 1909, Rutherford demonstrated the helium nature of the a-particle more directly than by deflection measurements (Fig. 529): He forced a considerable amount of radium emanation through the glass tube B by means of mercury into the narrow, extremely thin-walled glass tube A, completely air tight and able to withstand a gas pressure of one atmosphere. It was surrounded by another glass tube T, ending in the narrow glass tube V. The a-particles, emitted by the emanation, penetrated the thin wall of the tube A and assembled in the previously completely evacuated space T. By letting the mercury rise in T, it was possible to press the gas there into V for spectroscopic examination. Two days after placing the emanation into the tube A, the gas pressed into V displayed in a spectral instrument clear helium lines; if this was done after 6 days, the complete helium spectrum was obtained.

Extremely convincing is also the following experiment. The glass tube T is removed and the tube A surrounded by a thin lead sheet in open air. You leave the lead sheet for a few hours; you then melt it in a vessel and release from it the occluded gases, which again display the helium spectrum. Hence, the a-particles are propelled through the glass into the lead and again released by melting of the lead.

In radioactive minerals, which are so dense that gases cannot escape from them, helium has assembled in the course of geological time intervals in considerable quantities. Minerals have been discovered, which contained per gram up to 20 cm³ of helium. It is very probable that this helium was generated by the decomposition of radioactive substances. Hence the helium content yields estimates of the geological age of radioactive substances just by their lead content.

The large energy of the a-rays is also demonstrated by the thermal action. In the cases of a radium specimen, normally contained In a glass tube, all a-rays are absorbed by the substance itself or the glass. The absorption leads to appreciable heating of the specimen. Meier and Hess have shown in1912 that 1 g of radium develops by absorption of all its rays (including its decomposition products up to RaC) 140 cal/hr. The total amount of heat, which 1 g radium develops until it disintegrates completely into the stable final product corresponds to the combustion heat of 5000 kg coal. However, coal supplies its total energy instantaneously, while the energy stored in radium can only be utilized gradually in the course of thousands of years. At this stage (in 1935!), it seemed improbable that this disintegration could be accelerated and thus the thermal action of radioactive substances utilized practically.

Although radioactive substances are in Earth's crust only in small amounts - 1 g of its substance contains about 10^-13 g of radium - they have an important role in the maintenance and distribution of Earth's internal heat. Earth's loss of heat by radiation into outer space will already be covered, if the crust to a depth of 20 km contains the stated amount of radioactive substances.

Counting of a-particles

There exist two methods for counting individual a-particles - an electric and an optical one. Both of them have increased our knowledge of the nature of a-rays and atomic structure. The electric counter of Geiger 1913, which has become a simple measuring device, rests on the principle of magnification by collision ionisation of the initially small ionization effect of a-particles. A pointed wire D is introduced into the about 2 cm wide brass tube A (Fig. 530) by means of a plastic rubber plug E. The point of the wire lies about 1 cm from the disk B, which closes the tube. The rays to be counted enter the ionization space through the opening O into the middle of B. The brass tube is connected to the negative pole of an accumulator of about 1200 Volt, the wire leads to a thread electrometer, constructed much like a gold leaf electrometer. If you feed electric charge to the thread, it is attracted by the neighbouring plate. You can observe this motion either directly by microscope or record it photographically. (The thread electrometer is preferred to the gold leaf and quadrant electrometers, because it responds very quickly, which is very important for the present purpose.)

When an a-particle enters through O into the counter, it generates there a small number of positive and negative ions. The negative ions move towards the pointed wire and become very greatly accelerated, since the electric field intensity attains very high values near a sharp point. Hence each single ion, as it collides with the gas molecules, generates on its way to the point many hundreds of new ions which also multiply themselves in the same manner. In this way, you can magnify the initially very small primary ionization of an a-particle by a factor of millions, so that the electrometer receives from the point D a charge, which is large enough to provoke a clear movement of the thread of the electrometer. In order to make the thread after the entry of an a-particle into the counter return to its zero position, it is permanently earthed through a very high resistance through which the charge escapes.

Fig. 531 shows a photographic record of an a-radiation. The registering strip runs uniformly from down below to the top and is exposed as it passes the electrometer. If no a-particles enter the counter, the electrometer thread marks a line parallel to the strip, As an a-particle enters, the thread displaces to the right hand side (a b) and then returns corresponding to the discharge through the resistance to its normal position (b c). The left side of the strip displays marks of seconds. You see how irregularly the individual a-particles follow each other. After a longer interval, two or three particles follow close to each other. The statement that 1 mg uranium sends 1380 a-particles per minute must be interpreted as a statistical mean value. The actual number of particles during a single minute can deviate substantially from this mean value. Only counts taken over longer time intervals can yield reliable mean values.

In the optical counting method of Regner 1909, you bring the radioactive specimen which emits a-rays to within a few centimetres of a screen covered with phosphorescent zinc sulphide, which will light up brightly. The lighting is not uniform, but, as you can confirm with the aid of a magnifying glass, consists of short flashes of light (scintillations). These all along changing flashing scintillations are like a skye filled with stars. The emitted atoms cause by the might of their impacts lightning like glowing of the crystals. You can observe this in the case of every watch supplied with glowing numbers. For these numbers consist of zinc sulphide, mixed with a minute amount of radioactive substance, mostly radio-thorium. You see many thousands of light spots flash and everyone of them indicates the disintegration of an atom and formation of a new atom. And as they accumulate here and there, they reflect these oscillations, to which radioactive disintegration is subject. Counting of scintillations offers through their simplicity an important aid to the study of the nature of a-rays.

Half-time of radium

The half-time of many radioactive substances can be determined by measurement of the decrease of their activity. For others, for example, radium, this approach is impossible, because the disintegration is too slow. However, counting leads to the goal. At the end of a long tube R (Fig. 532), you fix an accurately weighed quantity of pure radium, at the other end the counter Z. In order that the a-particles emitted by M can reach the counter Z, the tube R must be evacuated. However, since the counter Z can only operate in air, the entrance opening O is covered with a very thin sheet of mica, which ensures an airtight wall between R and Z. If the area of the opening is a cm² and its distance from the specimen is r cm, then the number of a-particles entering the counter each second is N·a/4r²p, where N is the total number of a- particles emitted per second., because each second N·a/4r²p a-particles pass through 1 cm² at right angle to the direction of the rays and at the distance of r from the specimen, since in the case of an undisturbed trajectory the total number of emitted particles is distributed uniformly over a spherical surface with M as centre. Hence, if you count each second the a-particles which enter the counter, you can compute the total number N of all a-particles, emitted by the specimen.

Rutherford and Geiger determined in 1908 by experiments of this kind that 1 g of radium, pure and free of all its disintegration products - emanation, radium A, etc.,- emits each second 3.6·10¹⁰ a-particles. (The number of atoms which convert in 1 g of radium each second is just as large.) Hence you obtain the half-time: We know that 1 g of hydrogen contains 6.06·10²³ atoms; however, radium has 226 times the atomic weight of hydrogen, whence 1 g of radium contains 6.06·10²³/226 = 2.68·10²¹ atoms. Each second, 3.6·10¹⁰ atoms disintegrate, that is, the 1.34·10^-11th part of the total amount. This number tells us that 1640 years will elapse until 0.5 g of radium have disintegrated. The half-time of radium is therefore 1640 years.

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