Luminosity Units: UNIZOR.COM - Physics4Teens - Units in Physics - Base U...

Notes to a video lecture on http://www.unizor.com

For a short introduction to the International System of units (SI) see the previous lecture "SI Intro & Time" within this topic.

Luminosity Units

The purpose of this lecture is to introduce a measure of luminosity (luminous intensity) of some source of light.
This involves measuring the intensity of the source of light, spectral composition of this light, direction the energy of light is propagated and sensitivity of human eyes to different types of light.
Seems to be a very complicated task.

Let's start with a simpler concept of radiant flux. This is just an amount of energy emitted by some source of electromagnetic oscillations per unit of time, and it's measured in joules (watt per second).

The next step is a concept of luminous flux. It's different from radiant flux in what is related to a human eye's sensitivity to different wave lengths of electromagnetic oscillations.

The specialists that researched the eye sensitivity to light came up with a luminosity function that is an average among people and standardized distribution of eye's sensitivity to different wave lengths of light. This function is, obviously, zero for those wave lengths outside of a visible spectrum. Within a visible spectrum it has a bell shape with the maximum around wave length of green light - the light to which our eyes are most sensitive.

Two distribution functions on the above picture are for different lighting conditions with the red curve usually used for practical purposes.

Using this function, we define luminous flux Φ_lum(λ) of a monochromatic light of specific wavelength λ as a product of its radiant flux Φ_rad(λ) by luminosity function y(λ) for that wavelength.
For light that encompasses the whole spectrum of wavelengths we integrate the luminous flux for each wavelength to obtain the total luminous flux Φ_lum
Φ_lum = ∫_[0,∞]Φ_rad(λ)·y(λ)·dλ

The unit of luminous flux is called lumen (lm). Essentially, it's joules per second factored by the luminosity function.

Now let's talk about a direction of light since the light can be propagated differently in different directions.
Recall that angles on a plane are measured in radians (rad) with 1 rad being such an angle that, if used as a central angle in a circle of a radius R, will be subtended by an arc of the length R.
Solid angles in three-dimensional space are measured in steradians (sr) with 1 steradian (1 sr) being a part of space inside a cone such that, if this cone is placed inside a sphere with its vertex coinciding with the center of a sphere, it will be subtended by a part of sphere's surface of the area R².

Light from a source propagates in all directions. To deal with a possibility to emit different by brightness light in different directions we introduce luminosity as luminous flux per the unit of solid angle, steradian.
The unit for luminosity is called candela and
1 candela (cd) = 1 lumen (lm)
per 1 steradian (sr)

Historically, candela was, approximately, a luminosity of a candle of certain characteristics (size, shape, composition).

Realizing imperfectness of such a definition, later on candela was redefined as 1/60^th of the luminosity of 1 cm² of surface of melting platinum.

Finally, to get more precise definition, it was decided to define 1 candela as a base SI unit independently of eye sensitivity only for a specific monochromatic light of frequency 540·10¹² Hz (which is the light of the wavelength of about 555 nm - the green-yellow color, where eye sensitivity of most people is at maximum) as the one emitting radiant intensity in a particular direction equal to 1/683^rd joule.

The above definition gives a new unit of luminosity, candela (cd), about the same numerical value as it was defined previously, but puts it on a precise foundation.
Introduction of any particular luminosity function defines candela for other wavelengths.

Now if the light of 1 candela (abbreviation 1 cd) of the above frequency is uniformly propagated in all directions (there are 4π steradian in a sphere because its surface is 4πR²), the total radiant intensity will be
1 cd · 4π sr = 4π lumen (lm)

As an illustration, the luminosity of 800 candela can be obtained by an incandescent lamp that consumes 60 watt of energy per hour or by a fluorescent lamp consuming about 14 watts per hour, or by an LED lamp consuming about 10 watts per hour.

Amount of Substance: UNIZOR.COM - Physics4Teens - Units in Physics - Bas...

Notes to a video lecture on http://www.unizor.com

For a short introduction to the International System of units (SI) see the previous lecture "SI Intro & Time" within this topic.

Amount of Substance Units

Consider a rocket in space that works on hydrogen. It needs certain amount of hydrogen and certain amount of oxygen. Hydrogen, burning with oxygen, produces vapors of water and energy needed to move the rocket.
Hydrogen occurs in molecules of two atoms paired together as represented by formula H₂.
Similarly, molecules of oxygen also consist of two atoms O₂.

The molecule of water consists of two atoms of hydrogen connected with one atom of oxygen as represented by a structure H−O−H and formula H₂O.
Therefore, to make a reaction between molecules of hydrogen and oxygen, we have to take 2 molecules of hydrogen (2·H₂) for each molecule of oxygen (O₂).

So, the reaction we want to make in a rocket, operating with molecules, can be represented by the following equation
H₂ + H₂ + O₂ = 2·H₂O

From the practical viewpoint, how can we measure the proper quantities of hydrogen and oxygen to take on board in a rocket to make sure that all molecules will react with each other and there would be no excess of either gas?

A relatively good approach is to compare masses of atoms of hydrogen and oxygen.
An atom of hydrogen consists of a single proton in its nucleus and one electron flying on an orbit around a nucleus.
An atom of oxygen consists of eight protons and eight neutrons in a nucleus plus eight orbiting electrons.

For simplicity, assume that the mass of electrons in an atom is negligent relatively to the mass of proton or neutron, and masses of protons and neutrons are practically the same. We will correct this assumption later.
Therefore, we can say that the mass of one atom of oxygen is greater than the mass of one atom of hydrogen in approximately 16 times. Same proportion exists between their molecules because each molecule of either gas consists of two atoms.

Hence, there are as many molecules in 1 gram of hydrogen as in 16 grams of oxygen.
It's true for any other measure of mass, like kilogram or tonne. The proportion of the amounts of these two substances that contain the same number of molecules will always be 1:16.

Since we need two molecules of hydrogen for each molecule of oxygen to complete the reaction of all molecules, it seems reasonable to take 2 measures of hydrogen (by mass) per 16 measures of oxygen.

Generally speaking, if we deal with some substance that consists of uniform molecules X, and we know that the number of protons and neutrons of each such molecule is N_X, then in N_X grams (or any other unit of mass) of this substance will be the same number of molecules as in N_Y grams (or, correspondingly, other unit of mass) of substance Y that consists of molecules with N_Y protons and neutrons.

For example, a molecule of hydrochloric acid HCl contains one proton in the hydrogen atom plus 17 protons and 18 neutrons in the chlorine atom. This totals to 36 nucleons (protons+neutrons) per molecule of this substance.
The principle we spoke about states that in 36 units of mass of hydrochloric acid HCl there are approximately the same number of molecules as in 2 same unit of mass of molecular hydrogen H₂ or in 32 same units of mass of molecular oxygen O₂.

Experimentally it was determined that in N gram of any uniform substance, having N protons and neutrons in each molecule, there are about 6.02214076·10²³ molecules. This number is called Avogadro constant.

So, if a uniform substance has molecular weight (number of nucleons) N, its amount of N grams contains, approximately, Avogadro number of molecules. This amount of this substance is called a mole.

Thus, one mole of molecules of hydrogen (2 protons in a molecule H₂) is two grams, one mole of molecules of oxygen (8·2=16 protons, 8·2=16 neutrons in a molecule O₂) is 32 gram, one mole of molecules of carbon (6 protons, 6 neutrons in a molecule C) is 12 gram, one mole of hydrochloric acid (1+17=18 protons, 18 neutrons in a molecule HCl) is 36 gram.

The obvious improvement is to calculate the molecular weight precisely, taking into consideration all particles inside. The unit of atomic mass, as was discussed in earlier lectures, was 1/12^th of the mass of an atom of carbon-12. For example, the molecular weight of hydrochloric acid is not 36, but 36.458. So, strictly speaking, one mole of hydrochloric acid is 36.458 gram. This amount of acid contains Avogadro number of molecules.

To avoid imprecision, in 2019 there was a revision of the unit mole and physicists declared that one mole of any substance is EXACTLY the Avogadro number of its molecules.
That definition is much more precise and not connected to molecular weight, which is always approximate.

Temperature Units: UNIZOR.COM - Physics4Teens - Units in Physics - Base ...

Notes to a video lecture on http://www.unizor.com

For a short introduction to the International System of units (SI) see the previous lecture "SI Intro & Time" within this topic.

Temperature Units

As a prerequisite to this lecture, we suggest to familiarize yourself with the lecture "Temperature, Pressure and Volume of Ideal Gas" of the topic "Molecular Movement" in the chapter "Energy" of this course.

As we have established in that lecture, the temperature of some substance is a measure of kinetic energy of molecules of this substance. If we set a temperature of a substance with no movements of its molecules to zero, average kinetic energy of moving molecules of this substance is proportional to a substance temperature measured in some units. The coefficient of proportionality between the temperature and average kinetic energy of molecules is different for different substances under different conditions.

So, first of all, we have to assign the zero temperature to a state of a substance (or object) when all its molecules are at rest, which happens when there is no source of energy around, like in open space far from stars.

Secondly, we have to choose a unit of temperature.
Until recently the most popular scale of temperatures was Celsius (°C) with 0°C assigned to a temperature of melting ice and 100°C assigned to a boiling water with a unit of measurement being 1/100^th of a difference between these two points on a scale.
This same unit was used in a scale that starts with the absolute zero temperature called Kelvin scale.

Therefore, Kelvin scale for temperature was with zero temperature corresponding to a state of molecules at complete rest and a unit of measurement of the temperature was a degree with the distance between the temperature of melting ice and boiling water assigned as 100 degrees on this scale.

In 2019 this definition of units of measurement for temperature was revised in favor of defining a unit of temperature based on some physical constant.

For this purpose was chosen Boltzmann's constant introduced in the lecture referenced above that stated the inter-dependency of the main characteristics of ideal gas - pressure (p), volume (V), number of molecules (N) and absolute temperature (T) - the Combined Ideal Gas Law:
p·V/T = k_B·N
where
k_B = 1.380649·10⁻²³ (J/K)
is the Boltzmann's constant.

In the spirit of other redefinition of units in SI to be defined based on some physical constants, the value of Boltzmann's constant was postulated to be EXACTLY equal to 1.380649·10⁻²³ (J/K), which fixed the value of the unit of Kelvin temperature called kelvin (not a degree, as in Celsius).

Now the temperature of a substance with no molecular movement will be 0K.
Temperature of melting ice will be 273.15K (equivalent to 0°C).
Temperature of boiling water will be 373.15K (equivalent to 100°C).

Electric Current Units: UNIZOR.COM - Physics4Teens - Units in Physics - ...

Notes to a video lecture on http://www.unizor.com

For a short introduction to the International System of units (SI) see the previous lecture "SI Intro & Time" within this topic.

Electric Current Units

In the lecture "Magnetism of Two Parallel Straight Line Currents" of the topic "Magnetism of Electric Current" in the "Electromagnetism" chapter of this course we explained the existence of the force between two parallel wires with electric current running in them.
This force can be either attracting or repelling depending on the relative directions of the currents (the same or opposite).

Until recently, the force between two parallel wires was the base to establish the unit of electric current.
This definition was rejected in 2019 in favor of another, based a physical constant, according to the general approach to definition of units of measurement.

The unit of electric current ampere (A) was redefined based on a physical constant - the amount of electric charge of an electron (e).

The unit of electric charge, a coulomb (C), was, on one hand, defined by postulating that the charge of an electron equals to e=1.602176634·10⁻¹⁹C, where, on the other hand, an electric charge of 1 coulomb is an amount of charge going through a conductor with electric current of 1 ampere during the time of 1 second, that is 1C=1A·1s.

Taking ampere as a base unit and coulomb as derived, we can write
e=1.602176634·10⁻¹⁹A·1s
and, taking an amount of electric charge of an electron e as a given physical constant, we can derive an ampere as such an electric current that delivers e·10¹⁹/1.602176634 amount of electric charge per second.

Equivalently, we can say that an electric current of 1 ampere delivers 10¹⁹ electrons per 1.602176634 seconds.

Fractions of 1A have the same prefixes as with other units:
1 milliampere (1mA) = 10⁻³A
1 microampere (1μA) = 10⁻⁶A
1 nanoampere (1nA) = 10⁻⁹A
1 picoampere (1mA) = 10⁻¹²A

Multiples of 1A are
1 kiloampere (1kA) = 10³A
1 megaampere (1MA) = 10⁶A
1 gigaampere (1GA) = 10⁹A

Length Units: UNIZOR.COM - Physics4Teens - Units in Physics - Base Units

Notes to a video lecture on http://www.unizor.com

For a short introduction to the International System of units (SI) see the previous lecture "SI Intro & Time" within this topic.

Length Units

In the past the unit of length meter was defined as 1/10,000,000 of a distance from the north Pole to the equator.
Later on a metal rod made of an alloy of iridium and platinum of an X-shaped section was made as THE standard meter. A few copies were made to serve for all practical means stored in France and other places.


Obviously, as the requirements of different industries dictated more a more precision, this standard could not satisfy these demands.

In 1960 this standard was revised in favor of the one based on some fundamental physical constant.

Recall the main principle of establishing the units of measurement in the International System of units (SI) as being based on some constants that do not depend on our technology or any varying with time process (like rotation of the Earth).
That was the reason to define a time measuring unit second in SI as a period of time during which the number of oscillations of electromagnetic field of excited atom of cesium-133 is EXACTLY equal to 9,192,631,770 (see the previous lecture "Time" within this topic).

So, the definition of a time measuring unit second depends only on properties of an atom of a particular element, cesium-133, - a physical constant under wide range of conditions.

In the same spirit the unit of length meter (m) is defined in SI.
The process chosen for the role of a base for the standard unit of length is light and, in particular, its speed in vacuum, a constant independent of influence of any conditions.

The unit of length meter is defined using the already defined unit of time second as a distance the light in vacuum covers during an interval of 1/299,792,458 of one second.

Therefore, as follows from this definition, the speed of light in vacuum is EXACTLY 299,792,458 meters per second (m/s), and the main principle of defining the units of measurement through physical constants is preserved.

The abbreviation of the meter in SI is m.

Derived from the meter length unit are its fractions
1 decimeter (dm) = 10⁻¹ m
1 centimeter (cm) = 10⁻² m
1 millimeter (mm) = 10⁻³ m
1 micrometer (μm) = 10⁻⁶ m
1 nanometer (nm) = 10⁻⁹ m
1 picometer (pm) = 10⁻¹² m
as well as multiple unit
1 decameter (dam) = 10 m
1 hectometer (hm) = 100 m
1 kilometer (km) = 1000 m

SI & Units of Time: UNIZOR.COM - Physics4Teens - Units in Physics - Base Units

Notes to a video lecture on http://www.unizor.com

SI & Units of Time


Short Introduction to SI

Christopher Columbus has landed in the Bahamas in 1492, but was sure it's somewhere in Asia.
Historians attribute this mistake to a difference between Roman miles
(1 Roman mile ≅ 1.48 km)
and nautical ones
(1 nautical miles ≅ 1.85 km).

In September of 1999 NASA has lost a Mars Climate Orbiter spacecraft because its different components were made based on different units of measurement - most were made in metric units, but some were based on old English units.

There were other incidents, when incompatibility of components was caused by different units of measurement.

There is no need to explain the necessity to have common measuring units, so people can meaningfully communicate with each other.

In contemporary Physics we have an international system of units of measurement called SI.
A few lectures on this topic would conclude the course "Physics 4 Teens".

The SI units are divided into two categories - base units and derived units.

Base units are the units to measure the following quantitative physical characteristics:

time,
length,
mass,
electric current,
temperature,
quantity (of matter),
luminosity.

The most important aspect of defining physical units of measurement is to connect them to processes that to a high degree of certainty are constant in our world, like the frequency of electromagnetic oscillations emitted by a specific element or the speed of light in vacuum.

This approach is a reverse of an old one, when the units of measurement are defined subjectively.

Previously, the unit of time, the second, was defined as some fraction of a cycle of some concrete clock stored in a concrete place.
Analogously, the unit of length, the meter, was defined as the length of a concrete metal rod stored under some conditions in some laboratory in Paris.
This approach does not qualify for precise measurements because these "standard" second or meter are subject to change as the time goes on, conditions are slightly changing etc.

Instead, after measuring some objectively constant process, we define a unit of time or a unit of length as based on that process.


Time Units

The unit of time in SI is a second.
Historically, units of time were based on some astronomical observation, like a period of rotation of a Moon around our Earth or a period of rotation of the Earth around the Sun.
The problem was, these definitions are not constant because the rotations and their periods do change.

To make this unit of time really standard and independent of changing conditions of astronomical objects or concrete man-made clocks, the contemporary definition of the second in simple terms is as follows.

Physicists experimented with atoms of cesium-133 (⁵⁵Cs¹³³). Cesium is a soft metal with very low melting temperature of 28.4°C (83.1°F).
Their observation involved putting atoms of cesium-133 into a microwave beam of electromagnetic oscillations until the atoms vibrate in resonance. They have found the resonant frequency of these oscillations to be 9,192,631,770 oscillations per second. This is the frequency of photons that excite the outer electrons of a cesium atom to jump to an excited orbit.

Since the physical properties of this kind can be considered constant everywhere within a broad spectrum of conditions, it was decided that the good definition of a second can be based on this property.

The definition of a second in SI is that this is a period of time during which the number of oscillations of electromagnetic field that exited the atom of cesium-133, when it switches between the excited and ground level, is equal to 9,192,631,770.

This is a theoretical definition. From a practical standpoint, there is a device called a cesium clock that is the most precise time measuring instrument developed. This device was constructed and refined in 1950's by British physicist Essen.
Its precision was at the time one second in about 300 years. With subsequent modernizations, which also involved the analysis of a spin of cesium nucleus, the precision of cesium clock now is one second in more than a million years. The cesium clock is a very complicated device, it's specification is beyond the level of this course.

The abbreviation of the second in SI is s (sometimes, sec is used).

Derived from the second time unit are its fractions
1 millisecond (ms) = 10⁻³ sec
1 microsecond (μs) = 10⁻⁶ sec
1 nanosecond (ns) = 10⁻⁹ sec
1 picosecond (ps) = 10⁻¹² sec
as well as old familiar units
1 minute (min) = 60 sec
1 hour (hr) = 3600 sec

Fusion Basics: UNIZOR.COM - Physics4Teens - Atoms - Fusion

Notes to a video lecture on http://www.unizor.com

Fusion Basics

As we know, splitting (fission) of a nucleus of uranium-235 or plutonium-239 produces nuclei of combined mass smaller than initial mass of a nucleus of uranium-235 or plutonium-239.
It's called mass defect and it's the source of energy that can be used for different purposes, including, if not controlled, for making an atomic bomb.

Mass defect can be not only a result of a fission of nuclei of heavy elements, like uranium-235, but also from a fusion of light elements, as presented on this picture

Here an isotope of hydrogen with one proton and one neutron in a nucleus ¹H² called deuterium is fused with another isotope of hydrogen with one proton and two neutron in a nucleus ¹H³ called tritium.
The result of this fusion is an α-particle (that is, a nucleus of helium-4) ²He⁴ and free neutron ⁰n¹ which can be expressed as an equation
¹H² + ¹H³ = ²He⁴ + ⁰n¹

Let's evaluate a mass defect of this process of fusion.
Mass (in atomic mass units) of a nucleus ¹H² is 2.014 amu.
Mass of a nucleus ¹H³ is 3.016 amu.
So, total mass of the initial components of a fusion is 5.030 amu.
Mass of a nucleus ²He⁴ is 4.0015 amu.
Mass of a neutron ⁰n¹ is 1.00867 amu.
So, total mass of the products of a fusion is 5.010 amu.

As we see, the products of fusion have smaller mass (that is, smaller amount of matter) than the initial components. The mass defect is Δm=0.02 amu, which is converted into energy according to Einstein's formula E=Δm·c².


Problems in Fusion

The first problem is where to get the fusion components deuterium ¹H² and tritium ¹H³.
While deuterium is a stable isotope of hydrogen and can be extracted from water, tritium does not occur naturally and must be manufactured, which takes some energy.

The second problem is the physical conditions required for a reaction of fusion.
This reaction requires extremely high temperature (millions of degrees, like 100 million of °K) and pressure to squeeze the atoms to be within a very short distance from each other. To provide these conditions requires a lot of energy.

In attempts to create a controlled fusion physicists had to spend substantial amount of energy to achieve a successful fusion. Until recently, the net energy produced by controlled fusion was negative. However, some late experiments showed a small positive energy production. So, there is a hope of success in producing energy by controlled fusion.

On the other hand, uncontrolled fusion was achieved long time ago and implemented as an H-bomb. The needed temperature and pressure were provided by uncontrolled fission of uranium-235 or plutonium-239, described in the previous lectures.

Our Sun has the physical conditions required for a fusion to take place and plenty of necessary material for it - hydrogen. The energy emitted by Sun is the product of uncontrolled fusion.

Under these conditions different fusion reactions occur, not only deuterium to tritium. One of them involves hydrogen fused into helium through sequence of transformations, releasing energy as electromagnetic oscillations of different frequencies from γ-rays to infrared radiation:

(a) two nuclei of hydrogen are fused into a nucleus of deuterium emitting a positron (a positively charged anti-electron) and electrically neutral massless neutrino, releasing certain amount of energy on the way
¹H¹ + ¹H¹ → ¹H² + β⁺ + ν
where one of the protons of a hydrogen nuclei is transformed into a neutron and a positron with a neutrino as a by-product.

(b) the next reaction can occur between a freshly produced deuterium and hydrogen producing an helium-3 isotope, releasing certain amount of energy on the way
¹H¹ + ¹H² → ²He³

(c) two nuclei of a helium-3 isotope produced above fuse together forming a stable nuclei of helium-4 and hydrogen, releasing certain amount of energy on the way
²He³ + ²He³ → ²He⁴ + 2·¹H¹

At the end of this cycle, if we count all the participating nuclei, we see that from six nuclei of hydrogen a new nucleus of helium and two new nuclei of hydrogen are produced with certain amount of energy released on each step and different elementary particles emitted.

In a rather simplified form our Sun functions by burning hydrogen, producing helium and releasing energy on the way.

Provided temperature and pressure of Sun, many other nuclear reactions happened there, though they play a lesser role in producing energy.

Fission Basics: UNIZOR.COM - Physics4Teens - Atoms - Fission

Notes to a video lecture on http://www.unizor.com

Fission

Atoms of certain heavy elements, like uranium-235 or plutonium-239 are not very stable and can split into lighter elements if sufficient external force (like an absorption of a neutron) is applied.
This is called a nuclear fusion.

Below is one of the possible kind of a nuclear fission occurred when a neutron is captured by a nucleus of uranium-235.

This reaction can be described by a nuclear equation
⁰n¹ + ⁹²U²³⁵ →
→ ⁵⁶Ba¹³⁹ + ³⁶Kr⁹⁵ + 2·⁰n¹

Indeed, the number of protons on the left side of this equation is 0+92=92, which corresponds to this number on the right side 56+36+2·0=92.
The atomic number (number of protons and neutrons) on the left is 1+235=236, which corresponds to the right side 139+95+2·1=236.

The mass of a nucleus of uranium-235 is 235.043928 atomic mass units (amu).
The mass of a nucleus of barium-139 is 138.908841 amu.
The mass of a nucleus of krypton-95 is 94.939711 amu.
Neutron's mass is 1.007 amu.

The total mass of particles on the left side of equation is
1.007 + 235.043928 ≅
≅ 236.051 amu
The total mass of particles on the right side of equation is
138.908841 + 94.939711 +
+ 2·1.007 ≅ 235.863 amu


Mass Defect & Energy

As we see, in this reaction the resulting mass of fission components is less than the original mass. The difference in mass of 0.188 amu is the mass defect.
Where did this extra 0.188 amu go?
It's converted into energy released during this process of fission.

To calculate the energy that is released by the above process of fission, we use the famous Einstein's formula
E = m·c²
substituting the mass defect of 0.188 amu for mass m in this formula, where
1 amu ≅ 1.66·10⁻²⁷ kg
and speed of light in vacuum
c≅3·10⁸ m/sec.

The resulting amount of energy E_U235 released by the above reaction of fission of a single nucleus of uranium-235 is
E_U235 ≅
≅ 0.188·1.66·10⁻²⁷·9·10¹⁶ ≅
≅ 2.809·10⁻¹¹ J (joules)

An atom of uranium has mass of, approximately, 3.95·10⁻²² gram.
That means, there are, approximately, 0.253·10²² atoms in 1 gram of uranium.

Let's see how much energy can be released if all nuclei in the 1 gram of uranium-235 split into peaces as described above.
E_1gU235 ≅
≅ 2.809·10⁻¹¹·0.253·10²² ≅
≅ 0.711·10¹¹ J ≅ 20,000 kwh

Burning one gallon of gasoline produces about 4 kilowatt hours of energy.
Therefore, one gram of uranium-235, if all its atoms go through a fission process described above, produce an amount of energy equivalent to about 5,000 gallons of gasoline.


Fission Variants

The described above reaction of fission of uranium-235 is not the only one possible.
Under different environmental conditions and just by chance the fission of uranium-235 can produce different resulting components.

Here are a few examples.

⁰n¹ + ⁹²U²³⁵ →
→ ⁵⁶Ba¹⁴⁴ + ³⁶Kr⁸⁹ + 3·⁰n¹
where different isotopes of barium and krypton are produced.

⁰n¹ + ⁹²U²³⁵ →
→ ⁴⁰Zr⁹⁴ + ⁵²Te¹³⁹ + 3·⁰n¹
where zirconium and tellurium are produced.

⁰n¹ + ⁹²U²³⁵ →
→⁵⁷La¹³⁹+⁴²Mo⁹⁵+2·⁰n¹+7·e⁻
where 7 neutrons transformed into proton+electron pairs.

The components of fission can be different, the different is also an amount of energy released in each separate case.


Chain Reaction

The above examples of fission of a single nucleus of uranium-235, when it absorbs a single neutron, show that these reactions can produce more neutrons that one. If these two or three neutrons, in turn, are absorbed by other nuclei, those will split as well, producing more neutrons.

Under certain circumstances this might cause a chain reaction of fission.
These circumstances include, primarily, the amount of uranium-235, its purity and shape.

The picture below schematically shows how a fission of a single nucleus can cause a chain reaction of other nuclei around it, producing all kinds of fission products and new neurons that cause more fission reactions.


There is a concept of a critical mass for each element that can undergo the fission. Two primary elements used for peaceful (producing energy) and not peaceful (to make a bomb) purposes are
uranium-235 (⁹²U²³⁵) and
plutonium-239 (⁹⁴Pu²³⁹).
Critical mass
for uranium-235 is 47 kg,
for plutonium-239 it is 10 kg.
These numbers are approximate and are based on normal temperature, average density and spherical shape of a nuclear fuel mass.

Of course, the purity is also playing an important role, the greater the purity - the smaller critical mass required to initiate a chain reaction. For example, if uranium-235 represents only 20% of the total mass, the critical mass would be over 400 kg.

If the mass is less than critical, neutrons produced by a reaction of fission might just fly away, not absorbed by another nucleus.
If some kind of neutron reflectors are positioned around a mass of nuclear fuel, it increases the probability of such an absorption and decreases the critical mass, sometimes by a factor of 2.

Without any preventive measure, the chain reaction causes an explosion. That's how atomic bombs are working.

On the other hand, using neutron absorbers embedded into the mass of uranium-235 or plutonium-239, like graphite or boron, reduces the number and slows down the neutrons emitted by fission, which slows down or stops the chain reaction. That's how the nuclear power stations work.