Problem 1:

(a)  A telescope with a primary mirror with a diameter of 20 m records 314 photons/second from a star.  Assume that no photons are lost in our atmosphere and that the telescope plus detector system is 1% efficient.  What is the flux of photons/s/m²?
(b)  What is the energy flux in W/m² if the effective wavelength is 500 nm?
(c)  You observe this star for a year and see that it inscribes a small circle with diameter 1/3600 degrees relative to the fainter and much more distant stars.  The circular motion repeats with exactly one year period.  What is the distance to this star?  The Earth is 150 million km from the Sun.
(d)  How much energy does this star emit in all directions per second into the waveband that was detected (in part a)?

Problem 2:

A research reactor produces fluxes of neutrons to undertake measurements of the structure of materials.  The neutrons are emitted from an aperture in the reactor wall.  The beam contains a wide mixture of neutrons with different energies.  Bragg reflections by a crystal can be used to separate the a monoenergetic beam from the mixture in a similar way to how a diffraction grating separates colors of light into a monochromatic beam.
(a)  Suppose that Beryllium crystals with a Bragg plane spacing d = 1.80 Angstroms (1.8*10^-10m) are used to separate neutrons with an energy of 0.010 eV.  What is the de Broglie wavelength λ in Angstrom of a neutron with an energy of 0.010 eV?  Note that the neutrons are nonrelativistic.

(b)  Calculate the angle 2θ between the incident beam and scattered beam directions for this wavelength of neutrons based on the Bragg condition that the path difference for scattered neutrons is λ between successive crystal planes.

Problem 3:

For a classroom demonstration, you pass the beam from a HeNe laser (λ = 633 nm) through two identical, closely-spaced slits and observe the interference pattern on a wall 5 m away and perpendicular to the plane containing the slits.  In the darkened classroom, you can clearly observe up to 10 interference maxima on both sides of the central maximum, but the 4^th and 8^th maxima are missing on either side.  The spacing between adjacent maxima on the wall is 1.1 cm.
(a)  What is the spacing between the slits?
(b)  What is the slit width?

Problem 4:

In one dimension, a particle of mass m has potential energy U(x) = V cos(αx) - Fx, with V a positive constant.  Determine the frequency of small oscillations.  What relationship between V, α, and F makes oscillatory motion possible?

Problem 5:

A 3-kg sphere dropped through air has a terminal speed of 25 m/s.  Assume that the drag force is proportional to the velocity.  The sphere is attached to a spring of force constant 400 N/m and starts to oscillate with an initial amplitude of 20 cm.
(a)  When will the amplitude be 10 cm?
(b)  How much energy will have been lost when the amplitude is 10 cm?