Help!!!!!! We wish to calculate the de Broglie wavelength of an electron moving

Question

Help!!!!!!

We wish to calculate the de Broglie wavelength of an electron moving at relativistic speeds. One way to determine if relativity is a concern is to look at the speed of the particle: a rough guide is that relativistic calculations will be needed if the speed is greater than 10% the speed of light. Another way is to look at the kinetic energy of a particle: if the KE is more than about 10% of the mass energy, then a relativistic calculation is warranted. Consider an electron which has been accelerated through a potential of 600 KV. Its kinetic energy will therefore be 600 KeV. The electron's mass energy is 511 KeV, so using our criteria it is clear that relativity is needed. The de Broglie wavelength is lambda = h/p We might then find the momentum from the expression P = mv/ 1 - v2/c2 Equation 28.63 of the OpenStax textbook has the useful relationship E2 = (pc)2 + (mc2)2 We can write the de Broglie relationship as lambda = hc/pc we already know that he = 1240 eV-nm. If we can find pc in units of eV, it is then easy to find the wavelength. Find the value of pc for an electron with a kinetic energy of 600 KeV. Find the de Broglie wavelength of this electron.

Explanation / Answer

KE=(Y-1)mc^2

Y= sqrt(1-(v/c)^2)

given KE =600 Kev = 600*1.6*10^-19 J

substitue in above equation nd find v.

P= mv/Y

and

lambda = h/p.

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