Calculate the De-Broglie wavelength for electron accelerated across a potential of 10V, 100V, 1000V, and 10kV respectively. Which voltage experiment exhibits a larger fringe spacing in an interference experiment is performed?

a)

b)

c)  

d)

Explanation:

We know that the kinetic energy can be expressed in terms of momentum (p=  mv):

So, the momentum will be:

(1)

We can use the energy conservation to relate K and the electric potential energy. We assume that all potential energy becomes kinetic energy. Therefore:

(2)

a) If V=10 [V], K will be:

We can find the momentum using the equation (1)

The De-Broglie wavelength equation is given by:

(3)

b) If V=100 [V], using the same analyze, the De-Broglie wavelength will be:

c) V=1000 [V]

d) V=10000 [V]

The fringe spacing interference is proportional to the wavelength, so in our case, the larger fringe spacing occurs when voltage is 10 V, here λ = 3.87 angstroms.

I hope it helps you!

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explanation:

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