how to solve this question in detailed solution 1. [5 marks] Calculate the de Br

ID: 1458253 • Letter: H

Question

how to solve this question in detailed solution

1. [5 marks] Calculate the de Brogue wavelengths for the following three electron energies: 50 eV, 50 KeV, and 50 MeV. Use both the classical calculation and the relativistic calculation and compare the two answers. For the classical calculation you can get the momentum from the kinetic energy using K = p^2/2m. To obtain the momentum for the relativistic calculation, start with the two equations E^2 = (pc)^2 + (m0c^2)^2 and E = K + m0c^2 where E is the total energy and K is the kinetic energy and m0c^2 is the rest energy of the electron, 511 KeV.

Explanation / Answer

using classical calculation

K= p^2/(2m)

so, p^2= 2mK

so, p= sqrt (2mK)

de-broglie wavelength

lamda = h/sqrt [2mK]

by using relativistic calculation

pc^2 = E^2-(moc^2)^2

substituting E=K+moc^2

pc^2 = K^2 + 2K.moc^2

so, pc = sqrt[ K^2 + 2K.moc^2]

lambda = hc/pc

a. for electron K=50 eV

as m= 9.1 x 10^-31 kg

h= 6.626 x 10^-34 j.s

De-broglie wavelength = 1.6 x 10^-10 m

a. for electron K= 50 eV

lamda = 1239.84 eV.nm/pc (in eV)

= 1.7364 x 10^-10 m

b. for electron K = 50 KeV

De-broglie wavelength = 5.5 x 10^-12 m

b. for electron K= 50 KeV

De-broglie wavelength = 5.49 x 10^-12 m

c for electron K= 50 MeV

De-broglie wavelength= 1.6 x 10^-13 m

C. for electron K = 50 MeV

De-broglie wavelength = 1.7364 x 10^-13 m