A beam of electrons strikes a crystal at an anglewith the atomic planes, reflects of many atomic planes below the surface, and then passes into a detector also making anglewith the atomic planes. (a) If the minimumgiving constructive interference is. What is the ratio, Where is the spacing between atomic planes? (b) At what other angles, if any, would constructive interference occur?
(a) The ratio of given minimum angle is .
(b) Here can notbe considered as . So this is an invalid value of the.As a result, the only integer that exists is .This is the smallest angle at which constructive interference was detected. As a result, constructive interference is not visible from any other angles.
The angle of constructive interference.
When there is constructive interference, Bragg's equation can be used to describe the relationship between the quantities.
Using equation .
is the minimum angle for the constructive interference, so .
Therefore the ratio of is in the spacing between the atomic planes.
From Equation the minimum value for is .
Here m can notbe considered as . So this is an invalid value of the.
As a result, the only integer that exists is .
This is the smallest angle at which constructive interference was detected. As a result, constructive interference is not visible from any other angles.
A particle is connected to a spring and undergoes one-dimensional motion.
(a) Write an expression for the total (kinetic plus potential) energy of the particle in terms of its position x. its mass m, its momentum p, and the force constant of the spring.
(b) Now treat the particle as a wave. Assume that the product of the uncertainties in position and momentum is governed by an uncertainty relation . Also assume that because x is on average. the uncertainty is roughly equal to a typical value of . Similarly, assume that . Eliminate p in favor of x in the energy expression.
(c) Find the minimum possible energy for the wave.
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