1) a Beam of X-Rays of Wavelength 30 Pm Is Incident on a Calcite Crystal of Lattice Spacing

Physics 215 Test #2

March 1, 2007

Instructor: Julie Alexander

1)  A beam of x-rays of wavelength 30 pm is incident on a calcite crystal of lattice spacing 0.40 nm.

a)  Find the smallest angle between the crystal planes and the beam that will result in constructive reflection of the x-rays.

b)  What voltage must be applied to an x-ray tube for it to emit these x-rays?

2)  Show that , the fractional loss of energy of a photon during a Compton collision is given by . Where is the energy of the incident photon and is the frequency of the photon scattered through angle . You may use the Compton scattering formula, you don’t have to derive it from scratch.

3)  Find the phase velocity of an electron whose de Broglie wavelength is 15 pm.

4)  The phase velocity of a wave group is given by where g is the acceleration due to gravity, find the group velocity.

5) 

a)  Using Bohr’s hypothesis that an electron can circle a nucleus only if its orbit contains an integral number of de Broglie wavelengths, derive the radius of the nth Bohr orbit in terms of and quantum number n.

b)  Using the result of part (a), find the energy En of an electron in the quantum state n of hydrogen.

c)  Prior to the Bohr theory, Balmer found that one of the spectral series of hydrogen can be described by the empirical formula where R=1.097X107m-1 is the Rydberg constant. Using the result from part (b) write R in terms of and c.

6)  A light source is used to determine the location of an electron in an atom to a precision of 0.05nm. What is the uncertainty in the speed of the electron?

7)  A particle limited to the x-axis has the wave function between x=0 and x=1; elsewhere. Find the constant a.