De Broglie Wavelength and Relativistic Momentum

[Jacob87411]

Due to time constraints in AP physics we had to skip the chapter on realitivity and now we have problems in the next chapter that request us to use relativity:

At what energy will the nonrelativistic calculation of the de Broglie wavelength of an electron be in error by 5%?

Any help on exactly what this is even asking would be appreciated.

 

[Dr.Brain]

Error of 5% in calculation can be in calculation of 'mv' or momentum of electron as h is a constant .

According to me this is not a problem which has anything to do with relativity as the question says 'nonrelativistic' calculation.

as : mv = root of (2mE)

where m=mass of electron

here error will be in calculation of velocity .Use Heisenberg's principle

dx.dp>h/2pie

 

[dextercioby]

The HUP reads

$$\Delta x^{i}\Delta p_{j}\geq\frac{\hbar}{2}\delta^{i}_{j}$$

,but i don't see any to apply it,since u don't know the uncertainty in the position...

Daniel.

 

[jdavel]

Dr. Brain & dextercioby,

I think the 5% error they're talking about is the error resulting from using the classical momentum, mv, rather than the relativistic momentum, gamma*mv. Doesn't that seem right?

Jacob, gamma is the function of velocity that gives the increase in the inertia of an object when it is accelerated. This increase is one of the consequences of special relativity. Do you know the equation for gamma, or can you find it in the chapter on relativity that you skipped?