Electronvolt Unit Numerics: What to Choose?

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In summary: But the rest of the units will be different. You will have a new unit of mass, ##\mu##, and of length, ##\ell##, such that$$\mu = \frac{\hbar}{2.634638\times10^{-16}\ \mathrm{eV}\,\tau}$$and$$\ell = \left( \frac{\hbar}{2.634638\times10^{-16}\ \mathrm{eV}\,\tau} \right)^{1/2} = \frac{\hbar^{1/2}}{(2.634638\times10^{-16}\ \mathrm{eV}\,\tau)^{1/2}}$$
  • #1
aaaa202
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I'm doing some numerics on a system, where the relevant length scale is nanometers and energy scale is electronvolts. But are these two scales not affected by the choice of each other? I'm kind of confused. What should I choose as units for a system like mine.
 
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  • #2
aaaa202 said:
I'm doing some numerics on a system, where the relevant length scale is nanometers and energy scale is electronvolts. But are these two scales not affected by the choice of each other? I'm kind of confused. What should I choose as units for a system like mine.

they measure 2 totally different things
nanometres is a length measurement ( eg a physical distance, a wavelength etc)

electron Volt is a measurement of the energy of an electron ...
from wiki
In physics, the electronvolt[1][2] (symbol eV; also written electron volt) is a unit of energy equal to approximately 160 zeptojoules (symbol zJ) or 6981160000000000000♠1.6×10−19 joules (symbol J).Dave
 
  • #3
davenn said:
In physics, the electronvolt[1][2] (symbol eV; also written electron volt) is a unit of energy equal to approximately 160 zeptojoules (symbol zJ) or 6981160000000000000♠1.6×10−19 joules (symbol J).

Whoa, where did all those extra numbers and the spade come from!? When I copy the same line I get the following:

In physics, the electronvolt[1][2] (symbol eV; also written electron volt) is a unit of energy equal to approximately 160 zeptojoules (symbol zJ) or 1.6×10−19joules (symbol J).

aaaa202 said:
I'm doing some numerics on a system, where the relevant length scale is nanometers and energy scale is electronvolts. But are these two scales not affected by the choice of each other? I'm kind of confused. What should I choose as units for a system like mine.

No. An electronvolt is an amount of energy equal to moving a unit of charge equal to an elementary charge (the charge of an electron or proton) across a potential difference of 1 volt. Since the energy required to move an electron or proton through 1 volt does not depend on distance, the two scales do not affect one another.
 
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  • #4
Drakkith said:
Whoa, where did all those extra numbers and the spade come from!? When I copy the same line I get the following:

dunno LOL ... it's just the way it pasted for me in PF
I tried a couple of times and it wouldn't change so gave up and left as is :rolleyes::rolleyes:
 
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You have to be careful that you use the correct value for the fundamental constants. For instance, ħ would be in eV⋅s. If you write the equations with all the proper units, it should all be clear.
 
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  • #6
DrClaude said:
You have to be careful that you use the correct value for the fundamental constants. For instance, ħ would be in eV⋅s. If you write the equations with all the proper units, it should all be clear.

who was that directed to ? :smile:
 
  • #7
But SI the units of hbar are J*s = N*m*s
So in terms isn't hbar in units of nm equal to hbar(nm) = 10^9 * hbar(SI)
maybe I am just confusing myself.
 
  • #8
davenn said:
who was that directed to ? :smile:
The OP.
aaaa202 said:
But SI the units of hbar are J*s = N*m*s
So in terms isn't hbar in units of nm equal to hbar(nm) = 10^9 * hbar(SI)
Yes. Considering that ħ = 6.582119×10-16 eV⋅s, in a system of units where SI units are used everywhere except for length, which is in nm, and energy, which is in eV, ħ has a numerical value of 6.582119×10-7.

Edit: my comment that SI units are used everywhere except length and energy might not hold. I have to do a few checks first.
 
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  • #9
DrClaude said:
Yes. Considering that ħ = 6.582119×10-16 eV⋅s, in a system of units where SI units are used everywhere except for length, which is in nm, and energy, which is in eV, ħ has a numerical value of 6.582119×10-7.

Edit: my comment that SI units are used everywhere except length and energy might not hold. I have to do a few checks first.
Indeed, since E = ML2T-2, if E is in eV and L in nm, you need to modify the unit of mass or of time to get a consistent system.
 
  • #10
So is my above post (#3) incorrect then?
 
  • #11
Drakkith said:
So is my above post (#3) incorrect then?
You answered no to the question "But are these two scales not affected by the choice of each other?", which was correct, but your comment
Drakkith said:
Since the energy required to move an electron or proton through 1 volt does not depend on distance, the two scales do not affect one another.
is actually irrelevant. Choosing one Drakkith as the unit of energy would also work, however that is defined.

One can choose L = nm and E = eV and derive a consistent set of units. One can still choose for instance a unit of time or of mass, but not both, as otherwise the system of units will be inconsistent.
 
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  • #12
So will I be in good shape if I just use:
hbar = 10^9* hbar(in eV)
I am very confused, but I guess in the above I have redefined s=10^9 * s, i.e. a new unit of time.
 
  • #13
aaaa202 said:
So will I be in good shape if I just use:
hbar = 10^9* hbar(in eV)
No.

What you have is E = M L2 T-2, so T = (M L2 E-1)1/2, which gives a unit of time (lets call it ##\tau##)
$$
\tau = \left( \frac{\mathrm{kg}\ 10^{-18}\ \mathrm{m}^2}{1.602177 \times 10^{-19}\ \mathrm{J}} \right)^{1/2} = 2.498301\ \mathrm{s}
$$
So ħ = 6.582119×10-16 eV s becomes
$$
\hbar = 6.582119\times10^{-16}\ \mathrm{eV}\,\mathrm{s} \times \frac{\tau}{2.498301\ \mathrm{s}} = 2.634638\times10^{-16}\ \mathrm{eV}\,\tau
$$

If you decide to redefine mass instead of time, then ħ doesn't change: it is still ħ = 6.582119×10-16 eV s.
 

1. What is an electronvolt unit?

An electronvolt (eV) is a unit of energy commonly used in physics and chemistry. It represents the amount of energy gained or lost by an electron when it moves through an electric potential difference of one volt.

2. How is the electronvolt unit related to other units of energy?

The electronvolt is a very small unit of energy, equivalent to 1.602 x 10^-19 joules (J). It is often used to measure subatomic particle energies, while larger units like joules or kilojoules are used for macroscopic energies.

3. What are some common multiples and submultiples of the electronvolt unit?

Common multiples of the electronvolt include the mega-electronvolt (MeV), which is equivalent to one million electronvolts, and the giga-electronvolt (GeV), which is equivalent to one billion electronvolts. Submultiples include the kiloelectronvolt (keV), which is equivalent to one thousandth of an electronvolt, and the millielectronvolt (meV), which is equivalent to one thousandth of a keV.

4. How do I choose which electronvolt unit to use?

The electronvolt unit you choose to use will depend on the scale of energy you are working with. For example, if you are studying nuclear reactions, you may use MeV or GeV, while if you are studying atomic and molecular energies, you may use eV or keV. It is important to use the appropriate unit to avoid confusion and ensure accurate calculations.

5. Can the electronvolt unit be converted to other units of energy?

Yes, the electronvolt can be converted to other units of energy using conversion factors. For example, to convert eV to joules, you would multiply by the conversion factor 1.602 x 10^-19 J/eV. It is important to use the correct conversion factor to ensure accurate conversions.

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