A Question of De Broglie Waves?

[CollectiveRocker]

The problem states: By what percentage willl a non-relativistic calculation of the de Broglie wavelength of a 100-keV electron be in error? To start off the problem, I calculated the non-relativistic wavelength to be .124 m? If that number is correct, how do i move on?

 

[CollectiveRocker]

Can anyone explain the basic premise of the problem to me? I'm not asking for you to solve anything, just to get me off on the right track.

 

[wais]

To continue with the problem, we need to compare the non-relativistic calculation of the de Broglie wavelength with the actual or relativistic calculation. The actual or relativistic de Broglie wavelength can be calculated using the formula λ = h/mv, where h is Planck's constant, m is the mass of the electron, and v is its velocity.

In this case, we can calculate the relativistic de Broglie wavelength as follows:

λ = (6.626 x 10^-34 J·s) / (9.109 x 10^-31 kg) x (3 x 10^8 m/s)

= 2.74 x 10^-12 m

Now, we can calculate the percentage error in the non-relativistic calculation by using the following formula:

% error = (|actual value - calculated value| / actual value) x 100

= (|2.74 x 10^-12 m - 0.124 m| / 2.74 x 10^-12 m) x 100

= 99.995%

This means that the non-relativistic calculation of the de Broglie wavelength of a 100-keV electron will be in error by approximately 99.995%. This is a very large error and shows the importance of considering the relativistic effects when dealing with high energy particles like electrons.

In summary, to complete the problem, you have correctly calculated the non-relativistic de Broglie wavelength to be 0.124 m. Then, by using the formula for percentage error, we have calculated that this value will be in error by approximately 99.995% when compared to the actual or relativistic de Broglie wavelength.