Physics 202 Exam 4

In problems 1-6, you will receive credit only for the correct answer (no partial credit).

For fill-in-the-blank questions and problems, please place your answer in the indicated space. Be sure to include the correct units.

For multiple choice questions and problems, circle the letter for the correct answer. If your calculated answer is not approximately equal to one of those given, then you should circle "none of the above".

In problems 7-10, you will be graded on your work (with appropriate partial credit).

Last page is formula sheet, which also has physical constants.

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1. (5) In class we used a laser pointer to estimate the spacing between the spiral tracks on a DVD. Suppose that a blue-violet laser with a wavelength of 400 nm is used, and that the angular separation between the central maximum and the first-order maximum on either side is 30. What is the approximate spacing between the spiral tracks?

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2.(5) What is the energy of a photon in violet light with a frequency of Hz?

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3. (5) In Star Trek III, Mr. Spock correctly gave the electronic configuration of gadolinium as 1s2s2p3s3p4s3d4p5s4d5p6s5d4f. How many electrons are in the subshell with and ?

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4. (5) Suppose that the pupil of your eye is 2.5 mm in diameter. If you are seeing by light with a wavelength of 600 nm, what angular resolution is possible according to the Rayleigh criterion? (This is the minimum angle by which two objects must be separated in your field of view, in order for you to distinguish them as separate objects.)

In order to get credit, you must state whether the angle is measured in degrees or in radians!

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5. (5) An electron has a de Broglie wavelength of m. How fast is it moving? The mass of an electron is kg.

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6. (5) The ratio of the diameter of an atom to the diameter of its nucleus is roughly

(a) between 1 and 10

(b) between 10 and 100

(c) between 100 and 1000

(d) between 1000 and 10 000

(e) between 10 000 and 100 000

7. (17) A film of oil lies on a wet pavement. The refractive index of the oil is 1.50, and that of the water beneath it is 1.33. The film has the minimum nonzero thickness so that it appears dark due to destructive interference when viewed in light with wavelength = 700 nm in vacuum. What is the thickness of the oil film? (As usual, assume normal incidence for the light.)

8. (17) Calculate the wavelength of the X-rays emitted by silver, which has an atomic number of 47.

9. (18) Ultraviolet light with a wavelength of 120 nm shines on a metal surface. The photoelectrons that are emitted are found to have a maximum velocity of m/s. When ultraviolet light with an unknown wavelength shines on the surface, the maximum velocity is m/s. Calculate the value of .

  10. In this problem we will gently make our way through part of the Bohr theory of the hydrogen atom. Let be the radius of the electron's orbit, be the fundamental charge, be the electron's mass, be the electron's velocity, be the Coulomb's law constant, and

(a) (3) Write down the equation in which the centripetal force on the electron is equated to the Coulomb force.

(b) (3) Using the equation in part (a), solve for in terms of , , , and .

(c) (3) Write down Bohr's postulate for the quantization of angular momentum.

(d) (3) Using the equation in part (c), solve for in terms of , , , and the quantum number .

(e) (3) Set the two expressions for equal to each other, and solve for the allowed radii in terms of , , , , and . (The velocity should not occur in the expression for ; if it does you have not solved for in terms of and the fundamental constants.)

(f) (3) Calculate the smallest allowed value of , using kg, C, N m/C, J s (or J s).