# Units of length and time in MeV?

• philip041
In summary: But then you would get a different number for what 197.3 nm is, for example. In summary, converting a length given in MeV^-1 to SI units involves using the conversion factor of 1=197 MeV-fm and keeping in mind that hbar*c=1 in high-energy physics systems of units. This can also be approached as a simple unit conversion problem using fundamental constants such as hbar and c.
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

philip041 said:
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?

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

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

clem said:
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.)

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

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

So you have said hbar*c=1?

Sorry, I'm lost!

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.

philip041 said:
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".

Cheers I think I have it now!

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.

## 1. What does MeV stand for?

MeV stands for million electron volts. It is a unit of measurement used in physics to express energy or mass on the atomic or molecular scale.

## 2. How is MeV related to other units of energy and mass?

MeV is equivalent to approximately 1.602 x 10^-13 joules or 1.782 x 10^-30 kilograms. It is commonly used in nuclear and particle physics to express the masses and energies of subatomic particles.

## 3. How is MeV related to units of length and time?

MeV is not directly related to units of length and time. However, it can be used to measure the length of a particle's decay path or the time it takes for a particle to decay.

## 4. Can MeV be converted to other units of length and time?

No, MeV is a unit of energy or mass and cannot be converted directly to units of length or time. However, it can be converted to other units of energy or mass, which can then be related to units of length or time through various equations and formulas.

## 5. How is MeV used in practical applications?

MeV is commonly used in nuclear medicine to measure the energy of medical isotopes and in particle accelerators to describe the energies of subatomic particles. It can also be used in radiation therapy for cancer treatment, as well as in research on nuclear reactions and fundamental particles.

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