Mass in MeV ``` Name: Jake Status: student Grade: 9-12 Location: Outside U.S. Country: USA Date: Summer 2012 ``` Question: What does it mean when mass is expressed in MeV? When we see mass expressed in kilograms, no matter how small, we can at least get an inkling of what is meant. But in energy units? Replies: When dealing with “everyday” materials kilograms (or grams) is a convenient measure of mass. However, when the dealing with very small masses (The Higgs boson is a common such particle currently in the news.) it is more convenient to express the mass in terms of energy rather than kilograms, the numbers just get too large/small . The kilogram scale and the energy scale are related by: E = m x c^2. It does take some practice to get a “feel” for masses expressed, but that introductory inconvenience has a big payback of not having to deal with numbers containing very large/small trailing exponents. Vince Calder Jake The following calculations show that 1 MeV is equivalent to 1.780 x 10^-26 Grams Energy is the ability of a system to do work and is measured in Joules 1 electron volt (eV) = 1.6022 x 10-19 Joules (J) 1 (MeV) = 1.6022 x 10-19 x 106 = 1.6022 x 10-13 J Joules are a measure of work (Force x distance) 1 J = 1 Kilogram (Kgm) - meter2 (m2) / second2 (s2) = 1 Kgm-m2 / s2 = 1,000 gm-m2 / s2 = 1 x 103 gm-m2/s2 1 MeV =((1.6022 x 10-13 Kgm-m2) / s2) x 103 = 1.6022 x 10-10 gm-m2/s2 Energy = mass x (speed-of-light)2 E = m x c2 So, for your problem: m = E / C2 = 1 MeV / C2 = (1.6022 x 10-10 gm-m2/s2) / (3.0 x 108 m/s)2 = (1.6022 x 10-10 gm-m2/s2) / (9.0 x 1016 m2/s2) = ((1.6022/9) x 10-26 gm) = 0.1780 x 10-26 gm =1.780 x 10-27 gm More on eV’s at: http://en.wikipedia.org/wiki/Electronvolt#Mass Sincere regards, Mike Stewart Jake, br> Many times we are looking at charged particles that are accelerated to high velocities, and MeV (=Million electron Volts) is a way to express this energy that is convenient. It is confusing because it is a roundabout way to express energy, and it seems to say that “voltage” (in Volts) is equivalent to “energy” (in Joules) which it is not. Let us say we have two parallel plates of metal in which each side is connected to a battery. If the battery voltage is 1 Volt, then we say the “potential difference” between these plates is 1 Volt. If we take an electron and place it on the negative plate, we know that the electron will be attracted to the positive plate. If we let go of the electron and let it travel to the positive plate, it will gradually accelerate and gain energy until it hits the positive plate. The final energy of the electron when it hits the positive plate is called 1 electron-Volt. This energy can be converted to Joules, or actual units of energy, by multiplying it by the charge of an electron, or a very small number. 1 MeV= 1 million electron volts, so it would be the energy that the same electron would gain if we changed the battery voltage to 1 million volts and let it accelerate from the negative plate to the positive plate. Using electron volts is a matter of convenience, and it is not meant to confuse you. Particle physicists typically deal with very small particles, like electrons, and using electron-volts makes the calculations easier to handle. For example, to convert 1 electron volt to energy (in Joules), we need to multiply by the electron charge (.00000000000000000016 or 1.6x10^(-19) in scientific notation). This conversion results in a small number that is cumbersome to deal with, so it is simpler to talk of “electron-volts” instead of “Joules.” Kyle Bunch, PhD In particle physics, expressing masses as energies makes a lot of sense, because new particles are often created from the kinetic energies of collisions. The conversion factor is the speed of light c, from the mass-energy relation E = mc^2. The mass of an electron is 9.104e-31 kg or 511 keV; the mass of a proton is 1.6726e-27 kg or 938.28 MeV. Richard E. Barrans Jr., Ph.D., M.Ed. Jake, Describing mass in terms of eV is just a convention of units. You might find it useful to read an article about dimensional analysis to understand this answer -- it describes how you can easily transition among different units. Dimensional analysis is a very powerful and helpful tool in studying physics and engineering. Energy has units of mass times velocity squared (e.g. kg-m^2/s^2). Thus, if you divide energy by velocity squared, you are left with mass. Electron Volts are a unit of energy, but if you divide them by the speed of light squared, you are left with mass. When you are dealing with particle accelerators, it is convenient to measure particle energy in terms of eV. Once you have all your data in eV, it then becomes easier to describe mass in terms of eV (/c^2) rather than explicitly converting to SI units. Keep in mind that units are interchangeable -- there is not a single "correct" unit for a given measurement. 1000mg is equivalent to 1 gram. 0.001 gram is equivalent to 1 mg. You can measure a length in feet, meters, cubits, or any other unit you like. We choose one unit over another just for sake of ease and to make sure others can understand it (convention). It is easier to write 1 mg than it is to write 10^-3 kg (although perhaps sometimes 10^-3 kg is more appropriate). Hope this helps, Burr Zimmerman Hi Jake, You are not alone! Very small and very large energies may be difficult to visualize. You will get used to it. Energy and mass are linked. E =mc^2, or m = E/c^2. MeV is simpler to measure directly in devices that accelerate very small particles such as cyclotrons or colliders. Some simple conversions that help visualization are: 6 GeV approximates 1 nanojoule and 1 mm-mg(force) approximates 61 GeV or 61,000MeV. I try to imagine 61 billion little particles dragging around a one mg dust mite one mm (please ignore frictionals)... pretty doggoned small energy. Given that most of us at the Institute have pets, we can well imagine! Hoping this helps! Peter E. Hughes, Ph.D. Milford, NH Jake, According to Albert Einstein’s Theory of Relativity, and according to what happens in nuclear power plants and the Sun, mass can be expressed as energy (E=mc^2). The mass of an object can be viewed as energy stored in the object in the form of mass. When an atom experiences radioactive decay, the mass decreases. The energy released in forms such as motion, heat, and light equals the loss of mass multiplied by the square of the speed of light. Mass in energy units is the amount of energy that would be released if all of the object’s mass were converted into other forms of energy. Dr. Ken Mellendorf Physics Instructor Illinois Central College Click here to return to the Physics Archives

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