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catkin
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Homework Statement
The question is from Advanced Physics by Adams and Allday, section 8 Practice Exam Questions, question 30.
Estimate the de Broglie wavelength of an electron that has been emitted thermionically in a vacuum from a filament and then accelerated through a p.d. of 30.0 kV
Homework Equations
λde Broglie = h / p
E2 - p2c2 = m02c4
ETotal = m0c2 + K.E.
The Attempt at a Solution
I think the solution is valid; my concern is whether there is a better (= more elegant) way to do it.
The de Broglie wavelength is given by
λde Broglie = h / p
Where h is Planck's constant and p is momentum.
p could be found from p = γm0v but this would require finding v. More conveniently
E2 - p2c2 = m02c4
Where E is the total energy (E = m0c2 + K.E.)
Expanding E:
p2c2 = 2m0c2K.E. + K.E.2
Rearranging:
p = (1/c) √(2m0c2K.E. + K.E.2)
Substituting this p:
λde Broglie = hc / √(2m0c2K.E. + K.E.2)
Substituting values using SI units (including eV to J conversion factor 1.60E-19)
= 6.63E-34 * 3.00E+8 / Sqrt(( 2 * 9.11E-31 * 3.00E+8^2 * 30E+3 * 1.60E-19) + (( 30E+3 * 1.60E-19)^2 ))
= 7.0e-12 m ct2sf