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# UNITS!

eV. kilograms. UNITS!. Joules. m/s. Most physical quantities have units. You are probably already aware of the FUNDAMENTAL units for length, distance and time: meters (m), kilograms (kg), and seconds (s) You are also probably aware of the unit for energy: the joule (J).

## UNITS!

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1. eV kilograms UNITS! Joules m/s

2. Most physical quantities have units. You are probably already aware of the FUNDAMENTAL units for length, distance and time: meters (m), kilograms (kg), and seconds (s) You are also probably aware of the unit for energy: the joule (J). This unit is derived from the FUNDAMENTAL units for length, distance and time.

3. To see how this works, consider the formula for the energy of motion (kinetic energy): kinetic energy = ½mv2 A 2 kg mass moving at 1 m/s has kinetic energy = ½(2 kg)×(1 m/s)2 = 1 kg m2/s2 = 1 joule We say that the unit joule is derived from the units meters, kilograms and seconds: 1 J = 1 kg m2/s2

4. To get an idea of how much energy a joule represents, 100 J of energy would…

5. To get an idea of how much energy a joule represents, 100 J of energy would… …raise the temperature of 10 ml of water by about 2.4°C

6. To get an idea of how much energy a joule represents, 100 J of energy would… …raise the temperature of 10 ml of water by about 2.4°C …be the energy of motion (kinetic energy) of a hockey puck travelling at about 125 km/h

7. To get an idea of how much energy a joule represents, 100 J of energy would… …raise the temperature of 10 ml of water by about 2.4°C …be the energy of motion (kinetic energy) of a hockey puck travelling at about 125 km/h …be the energy you would get from the complete combustion of about 2 mg of gasoline

8. Although the joule is fine for measuring the amounts of energy we encounter in everyday experience, it is too big a unit to measure the energy of tiny particles. Instead, physicists use another unit called: The electron volt (eV).

9. To get an idea of how much energy an electron volt represents, if you were to take a 1.5 volt AAA battery out of your calculator (and were clever enough to make a small particle accelerator with it)…

10. To get an idea of how much energy an electron volt represents, if you were to take a 1.5 volt AAA battery out of your calculator (and were clever enough to make a small particle accelerator with it)…

11. To get an idea of how much energy an electron volt represents, if you were to take a 1.5 volt AAA battery out of your calculator (and were clever enough to make a small particle accelerator with it)… …you could give an electron 1.5 electron volts of energy. With a 9 volt battery, 9 electron volts, and so on.

12. If you want to convert from joules to electron volts, you must divide by 1.60×10-19.* So 1 joule of energy is equivalent to a whopping 6.25×1018 eV. Or, to put another way, 1 eV = 1.60×10-19 J. *This conversion factor is the charge of an electron, measured in another unit called the coulomb.

13. When it comes to mass, the kilogram is also much too big a unit to use for particles. Physicists often use units of energy (eV) to express mass, since you have seen that mass and energy are related by the formula E = mc2.

14. To see how this works, we can perform a short calculation: The mass of the electron is 9.1×10-31 kg. If we put the mass of the electron into the formula E = mc2, we get: E = (9.1×10-31 kg) ×(3×108 m/s)2 = 8.2×10-14 J ≈ 510000 eV = 0.51 MeV (Note: For 1.0 kg we would obtain 9.0×1016 Joules = 5.6×1035 eV !)

15. Now, if we do the same calculation for twice the mass of the electron: 2 × (9.1×10-31 kg) = 1.8×10-30 kg (≈ 10-30 kg) The energy of the two electrons would be: 2 × 0.51 MeV = 1.02 MeV (≈ 1 MeV) This gives us a handy approximate conversion factor: 1 MeV of energy for every 10-30 kg of mass.

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