RU2273057C1 - Plant for modeling radioactive disintegration - Google Patents

Abstract

FIELD: training appliances, possible use in laboratory practice sessions of physics course for studying physical laws and occurrences.

SUBSTANCE: exponential law of radioactive disintegration is modeled by means of integrating RC circuit, outputs of which are connected to inputs of voltage meter. Plant has base with image on face side of rectangle with label "particle counter", electric engine, moving bar with applied black rectangles of varying size, imitating amount of radioactive substance. On face side of base below rectangle with label "particle counter" first transparent window is positioned, imitating a vessel with radioactive substance. To the right from rectangle with label "particle counter" second transparent window is positioned for voltage meter.

EFFECT: possible visual modeling experiment using simple and cheap equipment without any possible threat to health.

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Description

The invention relates to educational devices and can be used in laboratory practice in higher and secondary special educational institutions at the rate of physics to study and deepen knowledge of physical laws.

A known laboratory setup for measuring the path of alpha particles and the decay rate of a source using an ionization chamber (Guide to laboratory studies in physics. Edited by L. L. Goldina. M: Nauka, 1973, p. 466, Fig. 246), containing source of radioactive substance, ionization chamber, Geiger-Muller counter and scintillation counter. It is impossible to visually experimentally verify the law of radioactive decay, because very long half-life of plutonium (2.44 · 10 ⁴ years).

There is also known an apparatus for studying the radioactive decay of a mixture of two isotopes (Evgrafova NN, Kagan VL Manual for laboratory work in physics. M: Higher school, 1970, p. 373 and 376), containing a source of radioactive substance, counter Geiger-Muller and the recalculation scheme. At this facility, one can investigate radioactive decay and take its characteristics.

On the considered installations, field experiments are carried out using expensive equipment and modern measuring equipment. The operation of such installations is associated with a hazard to the health of the student, which reduces the interest in learning.

The proposed installation allows you to conduct a visual model experiment on simple inexpensive equipment where there is no danger to health. The exponential law of radioactive decay is modeled using the simplest integrating RC circuit. In a model experiment, the presence of all the basic elements contained in a full-scale experiment is simulated: a source of a radioactive substance, a particle counter, and a count indicator.

The proposed installation can also be used for laboratory work when traveling to branches and representative offices in the correspondence form of training.

Closest to the proposed installation is an integrating circuit RC, the conclusions of which are connected to the inputs of the voltage meter (Zernov N.V., Karpov V.G. Theory of radio engineering circuits. M. - L .: Energy, 1965, p. 395, Fig. 8 -fourteen). On this device, the voltage across the capacitor increases exponentially, tending to the voltage of the DC source. The charge speed depends on the direct current of the RC circuit. This device allows you to simulate the law of radioactive decay. However, it is impossible to clearly demonstrate the process of radioactive decay, to remove its characteristics with different amounts of radioactive substance.

The aim of the invention is to expand the functionality of this device. This goal is achieved by introducing into it: a stand with an image on the front side of the rectangle with the inscription "particle counter"; an electric motor mounted on a stand; movable rail with black rectangles of different sizes, imitating the amount of radioactive substance; contacts mounted on the rail next to the corresponding black rectangles; the first transparent window simulating a vessel with a radioactive substance and located on the front side of the stand under a rectangle with the inscription "particle counter"; the second transparent window for the voltage meter display located on the front side of the stand to the right of the rectangle with the inscription "particle counter"; a first rectifier, the terminals of which are connected to the inputs of the integrating circuit RC; a second rectifier, the terminals of which are connected to the input of the electric motor; a white disc with black marks evenly spaced around its circumference, which is mounted on the axis of the electric motor in a plane parallel to the front of the stand; a fixed contact mounted on a stand and which is connected to the first input of the first rectifier; a step-down transformer, the first, second and third terminals of which are connected to the corresponding contacts of the movable rail, while the first and fourth terminals of the step-down transformer are connected to the inputs of the second rectifier, and the fourth terminal, in addition, is connected to the second input of the first rectifier; push-button switch that is connected to the inputs of the voltage meter.

Figure 1-3 shows drawings explaining the principle of operation of the proposed installation. Figure 4 shows a General view of the proposed installation.

The proposed installation contains 1 - integrating circuit RC; 2 - voltage meter; 3 - stand; 4 - electric motor; 5 - movable rail; 6 - a white disk with black marks located evenly around its circumference; 7 - fixed contact; 8 - the first rectifier; 9 - contacts; 10 - a rectangle with the inscription "particle counter"; 11 - the first transparent window; 12 - second transparent window; 13 - the second rectifier; 14 - step-down transformer; 15 - button switch.

The process of radioactive conversion obeys the law of radioactive decay:

where N ₀ is the number of nuclei at the initial moment, N is the number of non-decayed nuclei at time t, λ is the decay constant.

The initial number of nuclei in a radioactive substance with an arbitrary mass m is determined by the following expression:

where N _A is the Avogadro constant, M is the molar mass of the substance, determined by the formula: M = A × 10 ^-3 kg / mol. Here A is the mass number of the nucleus.

The number of nuclei decayed during time t is determined by the following expression:

в зависимости от времени для различных масс. По этим графикам можно определить период полураспада T_1/2, вычисляем: постоянную распадаFigure 1 shows graphs of the number of decayed polonium nuclei

depending on time for different masses. From these graphs you can determine the half-life T _1/2 , we calculate: the decay constant

average lifetime of a radioactive nucleus

initial activity

activity at time t

If you use the integrating circuit RC shown in figure 2, then it is possible to obtain dependencies similar to the curves shown in figure 1. The voltage measurement on the capacitor C as a function of time at various voltages of the DC source U ₀ occurs exponentially (Fig. 3):

The graphs in figure 3 are constructed without taking into account the factor K = 10 ²¹ . In order for dependences (3) and (8) to coincide without taking into account the factor K = 10 ^21, it is necessary to ensure equality in expressions (3) and (8) of the quantities:

период полураспада T_1/2=183 c, тогда используя формулу (4) находим λ=0,00379, а затем по формуле (9) определяем постоянную времени интегрирующей цепи RC: τ=RC=1/λ=263,85 c. Подбирая величины R и С можно обеспечить требуемую τ. Например, если принять R=1 МОм, то С=263,85 мкФ.For example, for polonium

half-life T _1/2 = 183 s, then using formula (4) we find λ = 0.00379, and then using formula (9) we determine the time constant of the integrating circuit RC: τ = RC = 1 / λ = 263.85 s. Choosing the values of R and C, we can provide the required τ. For example, if we take R = 1 MΩ, then C = 263.85 μF.

Thus, using the integrating circuit RC, a constant current source with voltage U ₀ and a voltage meter V, it is possible to simulate the process of determining the number of nuclei decayed over time t defined by expression (3). In this case

where K is a constant factor, U is the voltage measured at time t.

The number of decayed nuclei during time t will be removed from a voltmeter with digital indication during simulation. In this case, the data will need to be multiplied by the factor K (for the considered example, K = 10 ²¹ ).

The installation diagram for the simulation of radioactive decay is presented in figure 4. It contains an integrating circuit RC 1, the terminals of which are connected to the inputs of the voltage meter 2. In addition, the installation includes a stand 3, an electric motor 4, and a movable rail 5. A white disk 6 with black marks arranged uniformly around the disk circumference is installed on the axis of the electric motor 4. A fixed contact 7 is installed on the stand 3, which is connected to the first input of the first rectifier 8, and the terminals of the first rectifier 8 are connected to the inputs of the integrating circuit RC 1. Contacts 9 are installed on the movable rail 5. Black rectangles are shown near contacts 9 on the movable rail 5, which have different sizes and simulate the amount of radioactive substance. For example, if the first contact 9 of the rail 5 closes with the fixed contact 7, then the black rectangle on the rail 5 is the largest and, accordingly, the amount of radioactive substance will also be the largest.

On the front side of the stand 3 there is a rectangle 10 with the inscription “particle counter”, and under it is the first transparent window 11 that simulates a vessel with a radioactive substance. When the installation is off, through the first transparent window 11 one of the black rectangles is visible, depicted on the movable rail 5 and which simulates the amount of the investigated radioactive substance, as well as stationary black marks evenly spaced around the circumference of the white disk 6.

Next to the right of rectangle 10 with the inscription “particle counter” there is a second transparent window 12 for the display of the voltage meter 2. The voltage meter 2 itself is installed on the back of the stand 3 and is not visible, and only its display panel is visible through the second transparent window 12, where digits of the measured voltage are displayed. The digital display of the voltage meter 2 acts as an indicator of the particle counter. It fixes the number of decayed nuclei at the corresponding time according to expressions (8) and (10). Thus, everything located on stand 3 is not visible, but only what is in the first 11 and second 12 transparent windows is visible.

On the stand 3 is a second rectifier 13, the terminals of which are connected to the inputs of the electric motor 4.

To create the necessary voltages for the first 8 and second 13 rectifiers, the installation contains a step-down transformer 14. Its first, second and third terminals are connected to the corresponding contacts 9 of the movable rail 5. The first and fourth terminals of the step-down transformer 14 are connected to the inputs of the second rectifier 13, and the fourth terminal , in addition, connected to the second input of the first rectifier 8. Step-down transformer 14 is also installed on the back of the stand 3.

A push-button switch 15 is connected to the inputs of the voltage meter 2, when closed, the capacitor of the integrating circuit RC 1 is discharged. This is equivalent to setting the particle counter to the zero state.

Consider the work of the proposed installation in dynamics. To do this, install the movable rail 5 in the first position, as shown in Fig.4. In this case, the first contact 9 mounted on the movable rail 5 closes with the fixed contact 7. Through the first transparent window 11, the largest black rectangle shown on the movable rail 5 and located next to the first contact 9 will be visible. The black rectangle simulates the largest number a radioactive substance that is located at the bottom of a vessel with a radioactive substance.

When voltage is supplied to the step-down transformer 14 from the first and fourth terminals, voltage is supplied to the second rectifier 13. A constant voltage, taken from the second rectifier 13, is supplied to the electric motor 4. It drives the white disk 6 and, accordingly, the black marks uniformly around the circumference drive will run one after another. Through the first transparent window 11 we will see as if particles of radioactive decay will leave the radioactive substance (from the black rectangle) and rush to the rectangle 10 with the inscription "particle counter".

From the first and fourth terminals of the step-down transformer 14, through the closed contacts 7 and 9, a voltage is supplied to the first rectifier 8. This voltage is selected so that the output of the first rectifier 8 has a constant voltage U ₁₀ = 11.04 V, as shown in FIG. 2. Under the action of this voltage, the capacitor of the integrating circuit RC 1 is charged with a time constant τ = RC. Voltage meter 2 connected to the capacitor of the integrating circuit RC 1 shows the voltage changing over time. The time constant τ is chosen so that equality (9) holds. The digital board of the voltage meter, which is visible through the second transparent window 12, acts as an indicator of the particle counter and it records the number of decayed nuclei at the corresponding time according to expressions (8) and (10).

To repeat the experiment, press the button switch 15. In this case, the capacitor of the integrating circuit RC 1 is discharged through its contacts. Voltage meter 2 will show zero voltage. This is equivalent to resetting the particle counter to its original state.

To remove the dependence of the number of nuclei that decayed during time t, we use a laboratory stopwatch, which starts at the same time as the button switch 15 is pressed. Next, we determine the half-life T _{1/2 of} this graph (Fig. 1), and then all the values in accordance with the formulas ( 4), (5), (6) and (7).

If the movable rail 5 is shifted left first to the second, and then to the third position, then the second and then the third contact 9 closes with the fixed contact 7. The voltage from the second and fourth, and then from the third and fourth terminals is first removed from the step-down transformer 14. The output of the first rectifier 8 is formed, respectively, the voltage U ₀₂ , and then U ₀₃ (figure 2). Thus, we obtain the second and third dependencies (figure 3).

The technical and economic efficiency of the proposed facility is that in a model, simpler and cheaper experimental setup, the quality of mastering the basic laws and phenomena of physics by students is no worse than when conducting a full-scale experiment. Students have an increased interest in laboratory work, as no health hazard.

The proposed installation was implemented at the Department of Physics and is used in the educational process in laboratory classes in nuclear physics.

Claims (1)

Installation for modeling radioactive decay, containing an integrating RC circuit, the conclusions of which are connected to the inputs of the voltage meter, characterized in that a stand with an image on the front side of the rectangle with the inscription "particle counter", an electric motor mounted on the stand, a movable rail with applied black rectangles of different sizes, simulating the amount of radioactive substance, contacts mounted on a rail next to the corresponding black rectangles, the first transparent a window simulating a vessel with a radioactive substance and located on the front side of the stand under the rectangle with the inscription “particle counter”, the second transparent window for the voltage meter board located on the front side of the stand to the right of the rectangle with the inscription “particle counter”, the first rectifier, the conclusions of which connected to the inputs of the integrating circuit RC, a second rectifier, the terminals of which are connected to the inputs of the electric motor, a white disk with black marks, located evenly around its circumference, which mounted on the axis of the motor in a plane parallel to the front side of the stand, a fixed contact mounted on the stand and which is connected to the first input of the first rectifier, step-down transformer, the first, second and third terminals of which are connected to the corresponding contacts of the movable rail, while the first and fourth conclusions of the lowering the transformer is connected to the inputs of the second rectifier, and the fourth output, in addition, is connected to the second input of the first rectifier, a push-button switch, which is connected Input voltage to the meter.

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