S.2 A beam of electrons is created by accelerating electrons from rest through a
ID: 1326632 • Letter: S
Question
S.2 A beam of electrons is created by accelerating electrons from rest through a potential difference of 55 V. (a) What is the de Brogue wavelength of this batch of electrons? Express your result in nanometers. (b) Explain why it is not going to be easy to make two slits with a spacing that is roughly the same size as this wavelength. (Hint: the size of a typical atom is 0.1 nm.) (c) Find the de Brogue wavelength of a beam of protons instead of electrons accelerated through the same voltage difference (mc^2 = 938 MeV for a proton). Compare with your result in part (a). Is it going to be easier or harder to set up a two- slit interference experiment for protons?Explanation / Answer
a) De broglie wavelenth = h/P = h(/2mK.E.)1/2
K.E. of electron = eV,
=> De broglie wavelenth = h/P = h(/2meV)1/2
= 6.62*10-34 / ( 2*55*1.60*10-19 *9.1*10-31 )1/2
= 1.656 nm
b). we can't predict where a single electron will hit the screen, the only thing we know is that some places are more probable than others. th
c). for proton h/mv = 6.62*10-34 / ( 2*55*1.60*10-19 *1.67 × 10-27 )1/2 = .003917 nm
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