Question

Electrons with a speed of 1.1

Answer 1

de Broglie wavelength (?) associated with electron of (mass-m , v speed)
?e = h /p = h /me*ve >> p is momentum, e>electron
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h = 6.6*10^-34 Js
m (electron) = 9.1*10^-31 kg
?e = 6.6*10^-34 / 9.1*10^-31 * 1.1*10^6 meter
?e = 0.6593 *10^-9 meter
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fringe width
?x-e = D * ?e / d >>>
D is distance of screen, d = slit separation
?x-e = D * h / me * v *d -----(1)
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fringe width (spacing) when electron >> neutrons with same v
?x-n = D * h / mn * v *d -----(2) >>>>
n stands for neutron , e>electron
dividing
?x-n /?x-e = (me/mn)
= 0.00091x10^(-27) /1.6749 x 10^(-27) = 5.433*10^-4
?x-n = ?x-e * 5.433*10^-4
= 1.2 *10^-3 (meter) 5.433*10^-4
?x-n = 0.652 *10^-6 (meter) = 0.652 micrometers
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for different speeds and ?x-e = ?x-n = 1.2 mm
1.2 = D * h / me * ve *d
1.2 = D * h / mn * vn *d
dividing
1 = (mn/me) (vn/ve)
vn = ve* (mn/mn) = 2.3*10^6 = 2.3*10^6 m/s
speed of neutrons (vn)