ATOMS AND ATOMIC PHYSICS One of the most compelling demonstrations of wave-parti

Question

ATOMS AND ATOMIC PHYSICS

One of the most compelling demonstrations of wave-particle duality is the wave-like interference pattern displayed by electrons (which otherwise behave like a particle) when passing through a pair of double slits. If a beam of electrons is created by accelerating them from rest through a potential difference of just 500 V, and this beam is trained on a pair of slits 10 um apart with a detector 1 m behind the slits, what is the separation between adjacent bright spots on the screen?

Explanation / Answer

according to deBroglies hypothesis

wavelength lamda = h/(m*v) = h/p

and again using work done by potential difference = W = q*V = 0.5*m*v^2 = p^2/(2*m)

sqrt(q*V*2*m) = p

momentum p = sqrt(1.6*10^-19*500*2*9.11*10^-31) = 1.207*10^-23 kg m/s

then lamda = h/p = (6.625*10^-34)/(1.207*10^-23) = 5.5*10^-11 m

sepration between bright spots is y = lamda*L/d = (5.5*10^-11*1)/(10*10^-6) = 5.5*10^-6 = 5.5 um

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