Solving E=mc^2: What Units to Use?

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    E=mc^2 Units
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Discussion Overview

The discussion revolves around the appropriate units to use when applying the equation E=mc², particularly in the context of a mass of 43 kg. Participants explore whether to express energy in joules or electron volts, considering different contexts of application.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Al asks for clarification on whether to use joules or electron volts when calculating energy using E=mc².
  • Some participants assert that the SI unit of energy is joules, derived from the units of mass and speed of light used in the equation.
  • Others explain that electron volts are commonly used in high energy physics and atomic scales, requiring mass to be expressed in eV/c².
  • There is a suggestion that both joules and electron volts are valid units, depending on the scale of the system being analyzed.
  • Al expresses confusion about whether the unit should be J/kg or just J, indicating a lack of clarity on unit application.

Areas of Agreement / Disagreement

Participants generally agree that both joules and electron volts are units of energy, but there is no consensus on which unit is more appropriate for Al's specific calculation without further context.

Contextual Notes

There are unresolved questions regarding the application of units in different contexts, particularly the distinction between macroscopic and microscopic systems.

Allojubrious
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When solving with E=mc^2 what units should I use in the answer??
For example: (if I have an object with a mass of 43kg)
E=mc^2
E=(43kg)(299792458m/s)^2
E=3.86464727 × 10^18
Now here's my problem, do I include units of J/kg (joules per kilogram) or eV (electron volts)??
If someone could help me it would be very helpful.

Thanks,
Al
 
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What is the SI unit of energy?
 
Joules are kg*m2/s2. Since the units you chose for mass and c are kg, m and s, Joules are what you get.
 
Electron volts would require the mass to be given in {{eV}\over{c^2}}, which is common in high energy physics or when you're talking about atomic scale stuff. For example, the rest mass of a proton is 938 \times 10^8 {{eV}\over{c^2}}. By itself, eV is not an SI unit.
 
Oh ok so the unit would be J/kg, no?
Or would it just be J, because I read that it might be J/kg, so which one??
 
Allojubrious said:
E=(43kg)(299792458m/s)^2
E=3.86464727 × 10^18

1. What do you get with you multiply/divide the units together as indicated by your calculation? (Don't do any conversions!)

2. What is a joule (J) in terms of kg, m, and s?
 
The SI unit of energy is Joule.
eV is a convenient unit of energy in some areas of physics. The relationship between eV and Joule is
1eV = 1.6 x 10^-19 J
 
Oh alright so the unit would be Joule.

Thanks all,
Al
 
Last edited:
Either is correct, since joules and electron volts are both units of energy. If you are working with a macroscopic sized system, you probably want to use joules. If you are working with a microscopic system (i.e. single particles) then electron volts are probably more convenient.
 
  • #10
Khashishi said:
Either is correct, since joules and electron volts are both units of energy. If you are working with a macroscopic sized system, you probably want to use joules. If you are working with a microscopic system (i.e. single particles) then electron volts are probably more convenient.

Ah ok now that explanation makes a lot of sense thanks.

Al
 

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