A) An electron beam is passed between a set of double slits. What pattern does t

Question

A) An electron beam is passed between a set of double slits. What pattern does the particle model of light suggest we would see? What pattern does the wave model of light suggest we would see? What pattern is actually observed?

B) The electron beam is used again and this time instead of double slits we use diffecation gratings. The first grating only has a few slits per centimeter and the second grating has numerous slits per centimeter. Predict how the pattern of electrons hitting the screen beyond the gratings will appear for each grating> Give reasons for your predictions.

C) Next you keep the grating fixed and vary the electroc potential from the cathode to the anode to create the electron beam. Qualitatively predict how you think the pattern of the electrons hitting the screen changes and explain carefully the reasons for your prediction.

D) Compare and contrast a photon beam with an electron beam. What are the similar properties of both beams? What are the properties that only 1 beam possess?

Explanation / Answer

Part A)

The corpuscular model treats the electrons as particles, in this sense each particle passes through one of the slits and reaches the observation screen creating a single flash; after many flashes have a pattern passing through each slit, possibly centered on each slit with an intensity that decreases to turn away from each.

The wave model is the electron beam as a wave, in this case the beam passes through both slits building a pattern similar to that creates visible light interference, it has a maximum at the center between the cracks and lines of interference equally spaced light and dark.

The pattern observed in reality is described by the wave model, where the wavelength used must be predicted in the model of dual D'Broille

= h / mv

Part B)

The diffraction pattern beam is controlled to the relationship

d Sin = m (1)

where

d is the distance between two slits

m is the order of pattern

wavelength

In the case of the gratting with few lines per centimeter

d1 = 1 cm/ # lines1

n this case there is a single line for the angle of the equation 1. repeats this line-law increases the diffraction order (m), but the intensity decreases significztivamente

If gratting with many lines per centimeter

d2 = 1/# lines2

d2 < d1

as the value of the distance is less than the angle where the line appears is higher, also is repeated for each order, but the number of orders that appears to decrease the latter is close to = 90

in short, in both cases only lines are observed, but the value of the angle increases with the number of slots / cm

Part C)

To describe this case we use the expression of DeBroglie

= h / mv

Using Newton's second law

F = q E = m a

V =sqrt (2 qE/m x)

Where

q electron charge

E The electric field E

m mass of the electron

X acceleration distance

= h / m(sqrt (2 qE/m x))

as we can see the distance of acceleration is constant, by varying the electric field as the field increases the wavelength decreases ( ~ 1 / E1 / 2) for which the expression

d Sin = m

Sin = m / d

we can see that as decreases the angle is about 90 deg, so there is a limit value of m / d = 1 from which no diffraction pattern is observed

Part D)

There are marked similarities between the two beams

Photon electron bean

wave model wave model

---------- particule model

momentum=0 momentum<> 0

V = c V < c

charge =0 charge = e

E = h f E = ½ m v2

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