# Units of length and time in MeV?

#### philip041

How do you convert a length which has been given in MeV ^-1 to SI units?

Energy is mass length^2/time^2 so I guess it;s easy to make the steps of energy - mass - momentum etc... What about length and time?

Cheers

#### Doc Al

Mentor
How do you convert a length which has been given in MeV ^-1 to SI units?
Where have you seen length measured in such units?

#### clem

Length in MeV^-1 is used in high energy physics.
The conversion is 1=197 MeV-fm.

#### Redbelly98

Staff Emeritus
Homework Helper
From what I remember of this stuff, the units are such that
c = 1
hbar = 1
Energy units are MeV​

#### Doc Al

Mentor
Length in MeV^-1 is used in high energy physics.
The conversion is 1=197 MeV-fm.
D'oh! That totally slipped my mind. (Thanks guys.)

#### philip041

So if you multiply (100 MeV)^-1 by hbar*c and then divide by 197 x10^-12??

#### Doc Al

Mentor
1 (MeV)^-1 = 197 fm = 197 x 10^-15 m.

#### philip041

So you have said hbar*c=1?

Sorry, I'm lost!

#### Redbelly98

Staff Emeritus
Homework Helper
As this is a rather advanced topic, and the OP has made an attempt at wrapping his brain around what's going on, I'll take a stab at setting things up.

In any system of units, we can write
hbar * c = (a number) * (energy unit) * (length unit)​

where
(a number) = just that, some number
(energy unit) = the energy unit of interest
(length unit) = the length unit of interest

Specifically, in the high-energy physics systems of units, we have
(a number) = 1, since we have hbar=c=1 by definition
(energy unit) = MeV
(length unit) = unknown, to be solved for​

The value of hbar*c (or any physical constant for that matter) must be independent of the system of units being used. Therefore
hbar*c = (1.05e-34 J*s) * (3.00e8 m/s) = (energy unit) * (length unit)​
Since we know (energy unit) = 1 MeV, the above equation can be solved for (length unit).

EDIT:
Moreover, that length unit (conveniently expressed in SI units of fm) would be expressed as 1 MeV-1 in the high-energy units system, since
hbar * c = 1,​
by definition, in those units.

#### marcus

Gold Member
Dearly Missed
How do you convert a length which has been given in MeV ^-1 to SI units?
Google has a calculator that knows units like eV and automatically puts the answers in SI.

So the quickest way for you is just to use that online calculator and convert it directly.

You just go to Google as if you were going to do a search, and you type some expression into the ordinary Google box and press return.

For example suppose you type this into the box:
hbar*c/eV

The calculator knows what hbar is, and what c is. So it will compute that and tell you
"197.3 nanometers"

Or if you put this in:

2.0 hbar*c/MeV

then it will tell you "3.9 x 10-13 meters".

#### philip041

Cheers I think I have it now!

#### CompuChip

Homework Helper
If you want, you can view it just as a unit conversion.

For example, when you have 10 feet and want to convert it to meters, you multiply by some fixed constant K = 0.3048 meters / foot, to get
10 foot x 0.3048 (meters / foot) = 3.048 meters

When you have 197.3 nanometers (197.3 x 10^(-9) meter) you have to multiply by some other constant K'. We can make K' out of the fundamental constants c and hbar which occur in high-energy physics, by playing around with the units. We note that K' has to have units of energy / meter. Since hbar has units of energy * time and c has units of length / time, we easily see that we need to take K' = hbar c which gives a numerical value of K' = 1.973... × 10^(-16) GeV * meter. Then to express 197.3 nm in energy units, you just compute
$$\frac{197.3 \times 10^{-9} \text{ meter}}{1.973\cdots \text{ GeV meter}} = 10^{-9} \text{ GeV}$$
(= 1 eV).

The reason that all of this is actually useful, is for example that we have Einstein's special theory of relativity, which says that it actually makes sense to compare energy and mass.

However, if you are mentally disturbed you could make up new constants, like
p = 1237659,312398 GeV / quack
and express energy, time and length in terms of quacks.

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