Need help converting units, momentum of quark question

In summary, the minimum momentum of a quark confined in a proton can be estimated using the uncertainty relation and converting units to MeV/c. This calculation results in a value of approximately 100 MeV/c.
  • #1
DunWorry
40
0

Homework Statement


A proton has a diameter of about 1fm. Estimate the minimum momentum in units of MeV/C of a quark confined in a proton.


Homework Equations





The Attempt at a Solution



I used the uncertainty relation [itex]\Delta[/itex]P[itex]\Delta[/itex]X ~ [itex]\frac{\hbar}{2}[/itex]

[itex]\Delta[/itex]P ~ [itex]\frac{\hbar}{2 x 1x10^{-15}}[/itex] = 5.276x10[itex]^{-20}[/itex] kgm/s

I'm unsure how to put this into MeV/C

thanks
 
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  • #2
You can convert kg in J/c^2 and that to MeV/c^2. Isolate a factor of c (based on m/s) and use this to cancel one c in the denominator.

Alternatively, use ℏ given in MeV/c * length.
 
  • #3
mfb said:
You can convert kg in J/c^2 and that to MeV/c^2. Isolate a factor of c (based on m/s) and use this to cancel one c in the denominator.

Alternatively, use ℏ given in MeV/c * length.

Hmmmm I tried 5.276x10[itex]^{-20}[/itex] x (3x10[itex]^{8}[/itex])[itex]^{2}[/itex] = 4.7484x10[itex]^{-3}[/itex] Joules / c[itex]^{2}[/itex] Then to convert to eV I divided by 1.6x10[itex]^{-19}[/itex]

And I ended up getting 2.96775x10[itex]^{16}[/itex]eV / C. the answer should be around 200 MeV/C
 
  • #4
Did you consider m/s -> c?
If I divide your value by 3*108, I get 108eV/c or ~100MeV/c.
 
  • #5
Hmm that seems more correct, did I do the sum incorrectly?
 
  • #6
I don't see a sum, but a missing factor of 3*10^8 would explain the difference.
 
  • #7
mfb said:
I don't see a sum, but a missing factor of 3*10^8 would explain the difference.
I suspect that Dunworry is British (or learned "British" English) and they, for some strange reason, use the word "sum" to refer to any arithmetic calcluation!
 

FAQ: Need help converting units, momentum of quark question

1. How do I convert units for a momentum of quark question?

To convert units for a momentum of quark question, you will need to use the formula p = mv, where p is momentum, m is mass, and v is velocity. Make sure to use consistent units for mass and velocity, and then use the appropriate conversion factors to convert to the desired units.

2. What units are typically used for momentum of quark?

The most commonly used units for momentum of quark are kilograms (kg) for mass and meters per second (m/s) for velocity. However, depending on the context of the question, other units such as grams (g) or kilometers per hour (km/h) may also be used.

3. How do I calculate the momentum of a quark?

To calculate the momentum of a quark, you will need to know its mass and velocity. Then, you can use the formula p = mv, where p is momentum, m is mass, and v is velocity. Make sure to use consistent units for mass and velocity.

4. Can I use different units for mass and velocity when calculating momentum of quark?

No, it is important to use consistent units for mass and velocity when calculating momentum of quark. This is because the units for momentum are dependent on the units used for mass and velocity, and using different units will result in an incorrect calculation.

5. How do I convert between metric and imperial units for momentum of quark?

To convert between metric and imperial units for momentum of quark, you will need to use conversion factors. For example, 1 kilogram (kg) is equal to 2.20462 pounds (lbs), and 1 meter per second (m/s) is equal to 2.23694 miles per hour (mph). Use these conversion factors to convert the units accordingly.

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