That means that the constraint which determines the allowed orbits is 2 pi r = n

Question

That means that the constraint which determines the allowed orbits is 2 pi r = n lambda where, to remind you, n can only have a value that is a positive integer. Use your resources to help you answer these questions. Your mechanics text and your mechanics lab manual may be useful, as will the text for this semester. Use Eq. 10.2 and Eq. 10.3 to find an expression for v in terms of r and Using the expression you found for the electron's speed, and the fact that an electron in orbit around a proton has a centripetal force that can be described by -mv^2/r= -1/4 pi epsilon_0q^2/r^2 find an expression for r, the radius of the orbit in terms of n. You can simplify your expression for r using the substitution What are the value and units of a? What does a tell you about a hydrogen atom? Examine your expression for r. Does it have the correct units? What is the minimum radius possible? What is the maximum radius possible? Are all values of r possible? Are the allowed radii equally spaced? If not, do they get closer together or farther as increases? Thus far, you have used a model of an electron as a wave to find allowed values of angular momentum for an electron orbiting a proton, as in an atom of hydrogen.

Explanation / Answer

lambda = h/mv
2pir = n(lambda)

1. v = h/m(lambda) = n*h/m*2*pi*r
2. -mv^2/r = -q^2/4*pi*e*r^2
m(n^2*h^2)/(m^2*4*pi^2*r^2)*r = q^2/4*pi*e*r^2
(n^2*h^2)e/q^2(m*pi) = r
3. r = (n^2*h^2)e/q^2(m*pi) = (n^2)a
units of a = m, radius of hydrogen atom in ground state (n = 1)
4. Minimum radius possible = a
Max rad possible = infinity
No, only square of integer multiples of a are allowed
r get farther apart, (proportional to n^2)
  

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