Physical Science: GED Test Prep (page 4)
Physical science includes the disciplines of chemistry (the study of matter) and physics (the study of energy and how energy affects matter). The questions on the physical science section of the GED will cover topics taught in high school chemistry and physics courses. This article reviews the basic concepts of physical science—the structure of atoms, the structure and properties of matter, chemical reactions, motions and forces, conservation of energy, increase in disorder, and interactions of energy and matter.
The Structure of Atoms
You and everything around you are composed of tiny particles called atoms. The book you are reading from, the neurons in your brain, and the air that you are breathing can all be described as a collection of various atoms.
History of the Atom
The term atom, which means indivisible, was coined by Greek philosopher Democritus (460–370 B.C.). He disagreed with Plato and Aristotle—who believed that matter could infinitely be divided into smaller and smaller pieces—and postulated that matter is composed of tiny indivisible particles. In spite of Democritus, the belief that matter could be infinitely divided lingered until the early 1800s, when John Dalton formulated a meaningful atomic theory. It stated:
- Matter is composed of atoms.
- All atoms of a given element are identical.
- Atoms of different elements are different and have different properties.
- Atoms are neither created nor destroyed in a chemical reaction.
- Compounds are formed when atoms of more than one element combine.
- A given compound always has the same relative number and kind of atoms.
These postulates remain at the core of physical science today, and we will explore them in more detail in the following sections.
Protons, Neutrons, and Electrons
An atom is the smallest unit of matter that has a property of a chemical element. It consists of a nucleus surrounded by electrons. The nucleus contains positively charged particles called protons, and uncharged neutrons. Each neutron and each proton have a mass of about 1 atomic mass unit, abbreviated amu. An amu is equivalent to about 1.66 × 10–24 g. The number of protons in an element is called the atomic number. Electrons are negatively charged and orbit the nucleus in what are called electron shells.
Electrons in the outermost shell are called valence electrons. Valence electrons are most responsible for the properties and reaction patterns of an element. The mass of an electron is more than 1,800 times smaller than the mass of a proton or a neutron. When calculating atomic mass, the mass of electrons can safely be neglected. In a neutral atom, the number of protons and electrons is equal. The negatively charged electrons are attracted to the positively charged nucleus. This attractive force holds an atom together. The nucleus is held together by strong nuclear forces.
The number of protons in an element is always the same. In fact, the number of protons is what defines an element. However, the number of neutrons in the atomic nucleus, and thus the atomic weight, can vary. Atoms that contain the same number of protons and electrons, but a different number of neutrons are called isotopes. The atomic masses of elements in the periodic table are weighted averages for different isotopes. This explains why the atomic mass (the number of protons plus the number of neutrons) is not a whole number. For example, most carbon atoms have 6 protons and 6 neutrons, giving it a mass of 12 amu. This isotope of carbon is called "carbon twelve" (carbon-12).But the atomic mass of carbon in the periodic table is listed as 12.011. The mass is not simply 12, because other isotopes of carbon have 5, 7, or 8 neutrons, and all of the isotopes and their abundance are considered when the average atomic mass is reported.
An atom can lose or gain electrons and become charged. An atom that has lost or gained one or more electrons is called an ion. If an atom loses an electron, it becomes a positively charged ion. If it gains an electron, it becomes a negatively charged ion. For example, calcium (Ca), a biologically important element, can lose two electrons to become an ion with a positive charge of +2 (Ca2+). Chlorine (Cl) can gain an electron to become an ion with a negative charge of –1(Cl–).
The Periodic Table
The periodic table is an organized list of all known elements, arranged in order of increasing atomic number, such that elements with the same number of valence electrons, and therefore similar chemical properties, are found in the same column, called group. For example, the last column in the periodic table lists the inert (noble) gases, such as helium and neon—highly unreactive elements. A row in the periodic table is called a period. Elements that share the same row all have the same number of electron shells.
Some elements are frequently encountered in biologically important molecules and everyday life. Here, you will find a list of common elements, their symbols, and common uses.
H—Hydrogen: involved in the nuclear process that produces energy in the Sun, found in many organic molecules within our bodies (like fats and carbohydrates) and in gases (like methane)
He—Helium: used to make balloons fly
C—Carbon: found in all living organisms; pure carbon exists as graphite and diamonds
N—Nitrogen: used as a coolant to rapidly freeze food, found in many biologically important molecules, such as proteins
O—Oxygen: essential for respiration (breathing) and combustion (burning)
Si—Silicon: used in making transistors and solar cells
Cl—Chlorine: used as a disinfectant in pools and as a cleaning agent in bleach, and is also important physiologically as well, for example within the nervous system
Ca—Calcium: necessary for bone formation and muscle contraction
Fe—Iron: used as a building material; carries oxygen in the blood
Cu—Copper: a U.S. penny is made of copper; good conductor of electricity
I—Iodine: lack in the diet results in an enlarged thyroid gland, or goiter
Hg—Mercury: used in thermometers; ingestion can cause brain damage and poisoning
Pb—Lead: used for X-ray shielding in a dentist office
Na—Sodium: Found in table salt (NaCl), also important biologically within the nervous system and is a key player in the active transport process that occurs across cell membranes
Some elements exist in diatomic form (two atoms of such an element are bonded), and technically, they are molecules. These elements include hydrogen (H2), nitrogen (N2), oxygen (O2), fluorine (F2), chlorine (Cl2), bromine (Br2), and iodine (I2).
Structure and Properties of Matter
Matter has mass and takes up space. The building blocks of matter are atoms and molecules. Matter can interact with other matter and with energy. These interactions form the basis of chemical and physical reactions.
Molecules are composed of two or more atoms. Atoms are held together in molecules by chemical bonds. Chemical bonds can be ionic or covalent. Ionic bonds form when one atom donates one or more electrons to another. Covalent bonds form when the electrons are shared between atoms. The mass of a molecule can be calculated by adding the masses of the atoms that it is composed of. The number of atoms of a given element in a molecule is designated in a chemical formula by a subscript after the symbol for that element. For example, the glucose (blood sugar) molecule is represented as C6H12O6. This formula tells you that the glucose molecule contains six carbon atoms (C), twelve hydrogen atoms (H), and six oxygen atoms (O).
Organic and Inorganic Molecules
Molecules are often classified as organic or inorganic. Organic chemistry is technically defined as the study of carbon compounds. However, traditionally, certain compounds that contain carbon were considered inorganic (such as CO, carbon monoxide and CO2, carbon dioxide). In fact, a lot of chemists still consider these compounds to be inorganic. Many modern chemists consider organic molecules to be those that contain carbon and one or more other elements (such as hydrogen, nitrogen, and oxygen). Examples of organic compounds are methane (natural gas, CH4), glycine (an amino acid, NH2CH2COOH), and ethanol (an alcohol, C2H5OH). Inorganic compounds include sodium chloride (table salt, NaCl), ammonia (NH3), and water (H2O).
States of Matter
Matter is held together by intermolecular forces—forces between different molecules. Three common states of matter are solid, liquid, and gas. Matter is an atom, a molecule (compound), or a mixture. Examples of matter in solid form are diamonds (carbon atoms), ice (water molecules), and metal alloys (mixtures of different metals). A solid has a fixed shape and a fixed volume. The molecules in a solid have a regular, ordered arrangement and vibrate in place, but are unable to move far.
Examples of matter in liquid form are mercury (mercury atoms), vinegar (molecules of acetic acid), and perfume (a mixture of liquids made of different molecules). Liquids have a fixed volume, but take the shape of the container they are in. Liquids flow and their density (mass per unit volume) is usually lower than the density of solids. The molecules in a liquid are not ordered and can move from one region to another, through a process called diffusion.
Examples of matter in gaseous form include helium gas used in balloons (helium atoms), water vapor (molecules of water), and air (mixture of different molecules including nitrogen, oxygen, carbon dioxide, and water vapor). Gases take the shape and volume of the container they are in. They can be compressed when pressure is applied. The molecules in gases are completely disordered and move very quickly. Gas density is much lower than the density of a liquid.
Change of phase involves the transition from one state of matter into another. Freezing water to make ice for cooling your drink, condensation of water vapor as morning dew, and sublimation of dry ice (CO2) are examples of phase changes. A phase change is a physical process. No chemical bonds are being formed or broken. Only the intermolecular (physical) forces are affected.
Freezing is the process of changing a liquid into a solid by removing heat. The opposite process whereby heat energy is added to the solid until it changes into a liquid is called melting. Boiling is the change of phase from a liquid to a gas and also requires the input of energy. Condensation is the change from gas to liquid. Some substances sublime—change directly from the solid phase to the gas phase, without forming the liquid state first. Carbon dioxide is such a substance. Solid carbon dioxide, called dry ice, evaporates into the gas phase when heated. When gas changes directly into a solid, the process is called deposition.
The stronger the intermolecular forces are, the easier it is for the molecule to exist in one of the condensed states (liquid or gas) because these interactions among the molecules hold the solid or liquid together. For example, some neutral molecules have a positive end and a negative end even though, overall, the molecules have no net charge. Molecules such as these are considered polar and are attracted to each other by dipole-dipole forces. Molecules in which intermolecular forces are strong tend to have high boiling points, since these forces need to be overcome in order to turn the molecules into the gaseous state. This necessitates the input of more energy (heat).
Compounds and Mixtures
When two or more elements combine chemically, the result is a compound. Examples of compounds include carbon dioxide (a product of respiration),sucrose (table sugar), seratonin (a human brain chemical), and acetic acid (a component of vinegar). In each of these compounds, there is more than one type of atom, chemically bonded to other atoms in a definite proportion. The combination of these atoms also result in a fixed, definite structure.
When two or more elements combine physically, the result is a mixture. In a homogeneous mixture, the components can't be visually separated. Homogeneous mixtures also have the same composition (ratio of components) throughout their volume. An example is a mixture of a small amount of salt in water. A uniform mixture is often called a solution. In a solution, one substance (solute) is dissolved in another (solvent). In the salt and water mixture, the salt is the solute, and the water is the solvent. In a heterogeneous mixture, the components can often be visually identified, and the composition may vary from one point of the mixture to another. A collection of dimes and pennies is a heterogeneous mixture. A mixture of sugar and flour is also heterogeneous. While both components (sugar and flour) are white, the sugar crystals are larger and can be identified.
Miscibility is the term used to describe the ability of two substances to form a homogeneous mixture. Water and alcohol are miscible. They can be mixed in such a way that the mixture will be uniform throughout the sample. At each point, it will look, smell, and taste the same. Oil and water are not miscible. A mixture of these two substances is not homogeneous, since the oil floats on water. In a mixture of oil and water, two layers containing the two components are clearly visible. Each layer looks, smells, tastes, and behaves differently.
Removing stains from clothes, digesting food, and burning wood in a fireplace are all examples of chemical reactions. Chemical reactions involve changes in the chemical arrangement of atoms. In a chemical reaction, the atoms of reactants combine, recombine or dissociate to form products. The number of atoms of a particular element remains the same before and after a chemical reaction. The total mass is also preserved. Similarly, energy is never created or destroyed by a chemical reaction. If chemical bonds are broken, energy from those bonds can be liberated into the surroundings as heat. However, this liberation of energy does not constitute creation, since the energy only changes form—from chemical to heat.
Writing Chemical Reactions
A chemical reaction can be represented by a chemical equation, where the reactants are written on the left side and the products on the right side of an arrow that indicates the direction in which the reaction proceeds. The following chemical equation represents the reaction of glucose (C6H12O6) with oxygen (O2) to form carbon dioxide (CO2) and water (H2O). Your body runs this reaction all the time to obtain energy.
- (C6H12O6) + 6 (O2) → 6 (CO2) + 6 (H2O)
The numbers in front of the molecular formulas indicate the proportion in which the molecules react. No number in front of the molecule means that one molecule of that substance is reacting. In the previous reaction, one molecule of glucose is reacting with six molecules of oxygen to form six molecules of carbon dioxide and six molecules of water. In reality, there are many molecules of each of the substances and the reaction tells you in what proportion the molecules react. So if you had ten molecules of glucose react with 60 molecules of oxygen, you would obtain 60 molecules of carbon dioxide and 60 molecules of water. In many ways, chemical equations are like food recipes.
- 2 Bread + 1 Cheese + 2 Tomato → Sandwich
With two slices of bread, one slice of cheese, and two slices of tomato, you can make one sandwich. If you had six slices of bread, three slices of cheese, and six slices of tomato, you could make three sandwiches. The same principles of proportion apply in chemical reactions.
Types of Chemical Reactions
Similar reactions can be classified and categorized into specific types of reactions. For example, chemical reactions can be classified as synthesis reactions, decomposition reactions, single-replacement reactions, and double-replacement reactions. Each of these reactions proceeds as you may expect by its name.
A + B → AB
AB → A + B
C + AB → CB + A
AB + CD → AD + CB
Just as in the sandwich equation previously described, the reactants will always combine in specific ratios to form the product. If two slices of bread are on the left side of the equation, then the sandwich formed on the right side will always have two slices, never one or three. If fours slices are on the left side, then you will end up with four slices on the right.
Look at the following synthesis reaction:
There are two nitrogen atoms on both sides of the equation. Also, there are six hydrogen atoms on each side of the equation. Matter is conserved.
Now look at this synthesis reaction involving ions:
- 2F–+ Ca2+ → CaF2
In addition to showing the conservation of matter, this example shows the conservation of charge. The two fluoride ions, each with a charge of –1 combine with a calcium ion which has a charge of +2. The product formed is neutral—the two –1 charges and the one +2 charge cancel each other out—charge is conserved.
In fact, all chemical reactions must conserve:
- matter (mass)
- electric charge
Heat of Reaction (Enthalpy)
The breaking of molecular bonds releases energy stored in those bonds. The energy is released in the form of heat. Similarly, the formation of new bonds requires an input of energy. Therefore, a chemical reaction will either absorb or give off heat, depending on how many and what kind of bonds are broken and made as a result of that reaction. A reaction that absorbs energy is called endothermic. A container in which an endothermic reaction takes place gets cold, because the heat of the container is absorbed by the reaction. A reaction that gives off energy is called exothermic. Burning gasoline is a reaction that is exothermic—it gives off energy.
Increase in Disorder (Entropy)
Disorder, or entropy, is the lack of regularity in a system. The more disordered a system, the larger its entropy. Disorder is much easier to come by than order. Imagine that you have 100 blue beads in one hand and 100 red beads in the other. Now place all of them in a cup and shake. What are the chances that you can pick out 100 beads in each hand so that they are separated by color, without looking? Not very likely! Entropy and chaos win. There is only one arrangement that leads to the ordered separation of beads (100 blue in one hand, 100 red in the other), and many arrangements that lead to mixed-up beads (33 blue, 67 red in one hand, 33 red and 67 blue in the other; 40 blue, 60 red in one hand, 60 blue, 40 red in the other…). The same is true of atoms. Sometimes arrangement and order can be achieved. Atoms and molecules in solids, such as snowflakes, have very regular, ordered arrangements. But given enough time (and temperature), the snow melts, forming less ordered liquid water. So, although reactions that lead to a more ordered state are possible, the reactions that lead to disorder are more likely. The overall effect is that the disorder in the universe keeps increasing.
Often, a reaction needs help getting started. Such help can come from a catalyst. A catalyst is a substance or form of energy that gets a reaction going, without itself being changed or used up in the reaction. A catalyst acts by lowering what is called the activation energy of a reaction. The activation energy is often illustrated as a hill separating two valleys that needs to be crossed in order to get from one valley to the other (one valley representing the reactants, and the other the products). The catalyst acts by making the hill lower.
Light is a catalyst for the photosynthesis reaction. In living systems reactions are catalyzed by special protein molecules called enzymes.
Reversible and Irreversible Reactions
Some reactions can proceed in both directions—reactants can form products, which can turn back into reactants. These reactions are called reversible. Other reactions are irreversible, meaning that reactants can form products, but once the products form, they cannot be turned back into reactants. While wood can burn (react with oxygen) to produce heat, water, and carbon dioxide, these products are unable to react to form wood. You can understand reversibility better if you look at the activation energy diagram in the previous section. The hill that needs to be crossed by reactants to form products is much lower than the hill that needs to be crossed by products to form reactants. Most likely, such a reaction will be irreversible. Now look at the following diagram. The hill that needs to be crossed is almost the same for reactants and for products, so the crossing could take place from both sides—the reaction would be reversible.
Motions, Forces, and Conservation of Energy
A force is a push or a pull. Objects move in response to forces acting on them. When you kick a ball it rolls. A force is also required to stop motion. The ball stops rolling because of the frictional force. What happens here? First your body breaks the chemical bonds in the food you have eaten. This supplies your body with energy. You use up some of that energy to kick the ball. You apply a force, and as a result the ball moves, carrying the energy your foot supplied it with. But some of that energy is transferred from the ball to the ground it rolls on in the form of heat, due to the frictional force it encounters on the surface of the ground. As energy is lost this way, the ball slows down. When all of the energy is used up through friction, the ball stops moving. This example illustrates the concept of conservation of energy, as well as Newton's first law—the Law of Inertia.
What is the difference between speed and velocity? A speed, such as "30 miles per hour," has magnitude. A velocity has magnitude and direction (30 miles per hour, north). A similar distinction can be made in considering the difference in the terms distance and displacement. If you walk 20 feet to your mailbox and 20 feet back, the distance you traveled is 40 feet. Your displacement is zero, because displacement compares your ending point to the starting point.
Velocity is defined as the displacement divided by elapsed time. When you look at the change in velocity divided by the elapsed time, you are looking at acceleration. An acceleration that is negative (due to an ending velocity that is less than the starting velocity) is called a deceleration. For velocity of motion to change, either the speed and/or the direction must change and a net or unbalanced force must be applied. To summarize, an object at rest (whose speed is zero) remains at rest, unless some force acts on it—a person pushes it, the wind blows it away, gravity pulls it down… An object that is moving continues to move at the same speed in the same direction, unless some force is applied to it to slow it down, to speed it up, or to change its direction. The amount of acceleration or deceleration is directly proportional to the force applied. The harder you kick the ball, the faster it will move. The mass of the ball will also determine how much it will accelerate. Kick a soccer ball. Now kick a giant ball made of lead with the same force (watch your foot!). Which ball moves faster as a result of an equal kick? These observations constitute Newton's second law—the Law of Acceleration.
A good way to learn about the laws of motion is to shoot pool. What happens to billiard balls if you miss and fail to hit any of them? Nothing. They stay at rest. What happens when you hit the cue ball with the cue? It moves in the direction you hit it in. The harder you hit it, the faster it moves. Now, what happens when the cue ball collides with another ball? The other ball starts moving. The cue ball slows down. The energy is transferred from the cue ball to the ball it collided with. When an object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object. This is Newton's third law—the Law of Interaction.
Types of Forces
Newton's laws do not depend on the type of force that is applied. Some types of forces include gravitational, electromagnetic, contact, and nuclear.
Gravitation is an attractive force that each object with mass exerts on any other object with mass. The strength of the gravitational force depends on the masses of the objects and on the distance between them. When we think of gravity, we usually think of Earth's gravity, which prevents us from jumping infinitely high, keeps our homes stuck to the ground, and makes things thrown upward fall down. We, too, exert a gravitational force on the Earth, and we exert forces on one another, but this is not very noticeable because our masses are very small in comparison with the mass of our planet. The greater the masses involved, the greater the gravitational force between them. The Sun exerts a force on the Earth, and the Earth exerts a force on the Sun. The moon exerts a force on the Earth, and the Earth on the moon. The gravitational force of the moon is the reason there are tides. The moon's gravity pulls the water on Earth. The Sun also exerts a force on our water, but this is not as apparent because the Sun, although more massive than the moon, is very far away. As the distance between two objects doubles, the gravitational force between them decreases four times.
What is the difference between weight and mass?
On Earth, the acceleration due to gravity, g, is –9.8 m/s2.Your weight (w) is really a force. The formula F = ma becomes w = mg. Since the acceleration, g, is –9.8 m/s2, the overall force (w) is negative, which just means that its pull is in the downward direction: The Earth is pulling you towards its center. You have probably heard somebody say: "You weigh less on the moon!" This is true because the gravitational force on the moon is less than the Earth's gravitational force. Your mass, however, would still be the same, because mass is just a measure of how dense you are and the volume you take up.
Electricity and magnetism are two aspects of a single electromagnetic force. Moving electric charges produce magnetic forces, and moving magnets produce electric forces. The electromagnetic force exists between any two charged or magnetic objects, for example, a proton and an electron or two electrons. Opposite charges attract (an electron and a proton) while like charges repel (two protons or two electrons). The strength of the force depends on the charges and on the distance between them. The greater the charges, the greater the force. The closer the charges are to each other, the greater the force between them.
Contact forces are forces that exist as a result of an interaction between objects, physically in contact with one another. They include frictional forces, tensional forces, and normal forces.
The friction force opposes the motion of an object across a surface. For example, if a glass moves across the surface of the dinner table, there exists a friction force in the direction opposite to the motion of the glass. Friction is the result of attractive intermolecular forces between the molecules of the surface of the glass and the surface of the table. Friction depends on the nature of the two surfaces. For example, there would be less friction between the table and the glass if the table was moistened or lubricated with water. The glass would glide across the table more easily. Friction also depends on the degree to which the glass and the table are pressed together. Air resistance is a type of frictional force.
Tension is the force that is transmitted through a rope or wire when it is pulled tight by forces acting at each end. The tensional force is directed along the rope or wire and pulls on the objects on either end of the wire.
The normal force is exerted on an object in contact with another stable object. For example, the dinner table exerts an upward force on a glass at rest on the surface of the table.
Nuclear forces are very strong forces that hold the nucleus of an atom together. If nuclei of different atoms come close enough together, they can interact with one another and reactions between the nuclei can occur.
Forms of Energy
Energy is defined as the ability to do work. In addition, energy can't be created or destroyed. Energy can only change form. Forms of energy include potential energy and kinetic energy.
Potential energy is energy that is stored. Kinetic energy is the energy associated with motion. Look at the following illustration. As the pendulum swings, the energy is converted from potential to kinetic, and back to potential. When the hanging weight is at one of the high points, the gravitational potential energy is at a maximum, and kinetic energy is at the minimum. At the low point, the kinetic energy is maximized, and gravitational potential energy is minimized.
Examples of potential energy include nuclear energy and chemical energy—energy is stored in the bonds that hold atoms and molecules together. Heat, hydrodynamic energy, and electromagnetic waves are examples of kinetic energy—energy associated with the movement of molecules, water, and electrons or photons (increments of light).
Interactions of Energy and Matter
Energy in all its forms can interact with matter. For example, when heat energy interacts with molecules of water, it makes them move faster and boil. Waves—including sound and seismic waves, waves on water, and light waves—have energy and can transfer that energy when they interact with matter. Consider what happens if you are standing by the ocean and a big wave rolls in. Sometimes the energy carried by the wave is large enough to knock you down.
Energy is also carried by electromagnetic waves or light waves. The energy of electromagnetic waves is related to their wavelengths. Electromagnetic waves include radio waves (the longest wavelength), microwaves, infrared radiation (radiant heat), visible light, ultraviolet radiation, X-rays, and gamma rays. The wavelength depends on the amount of energy the wave is carrying. Shorter wavelengths carry more energy.
When a wave hits a smooth surface, such as a mirror, it is reflected. Sound waves are reflected as echoes. Matter can also refract or bend waves. This is what happens when a ray of light traveling through air hits a water surface. A part of the wave is reflected, and a part is refracted into the water.
Each kind of atom or molecule can gain or lose energy only in particular discrete amounts. When an atom gains energy, light at the wavelength associated with that energy is absorbed. When an atom loses energy, light at the wavelength associated with that energy is emitted. These wavelengths can be used to identify elements.
In a nuclear reaction, energy can be converted to matter and matter can be converted to energy. In such processes, energy and matter are conserved, according to Einstein's formula E = mc2, where E is the energy, m is the mass, and c is the speed of light. A nuclear reaction is different from a chemical reaction because in a nuclear reaction the particles in nuclei (protons and neutrons) interact, whereas in a chemical reaction, electrons are lost or gained by an atom. Two types of nuclear reactions are fusion and fission.
Fusion is a nuclear process in which two light nuclei combine to form one heavier nucleus. A fusion reaction releases an amount of energy more than a million times greater than the energy released in a typical chemical reaction. This gain in energy is accompanied by a loss of mass. The sum of the masses of the two light nuclei is lower than the mass of the heavier nucleus produced. This mass defect (the difference between the expected mass and the actual mass) is the m in Einstein's formula, and depending on how big m is, a proportional amount of energy will be released. Nuclear fusion reactions are responsible for the energy output of the Sun.
Fission is a nuclear process in which a heavy nucleus splits into two lighter nuclei. Fission was used in the first atomic bomb and is still used in nuclear power plants. Fission, like fusion, liberates a great amount of energy. The price for this energy is a loss in mass. A heavy nucleus that splits is heavier than the sum of the masses of the lighter nuclei that result.
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