Document 2378550

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Li.
Barnard's star, named after the American astronomer Edward E. Barnard, is an orange star in the constellation Ophiuchus.
It has the
largest known proper motion (/1 = 10.31" yr-l) and the second- largest
parallax angle (p = 0.552"). In the spectrum of Barnard's star, the He>
absorption line is observed to have a wavelength of 6560.44 A.
5.
(a)
Determine the radial vcloci ty of Ba,rnard
(b)
Determine the transverse velocity of Barnard's
(c)
Calculate the speed of Barnard's
'8
star.
star.
star through space.
\Vhen salt is sprinkled on a flame, yellow light consisting of two closely
spaced wavelengths, 5889.97 A and 5895.94 A, is produced. They are
called the sodium D lines and were observed by Fraunhofer in the Sun's
spectrum.
If this light falls on a diffraction grating with 300 lines per millimeter, what is the angle between the second-order spectra of
these two wavelengths?
How many lines of this grating rIlUst be illuminated for the sodium
D lines to just be resolved?
6. PrOVE' that
he = 12400 e V
A.
.X
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.-'
.2
Consider the ca..'3eof a "collision" between a photon and a free proton,
initially at rest. What is the characteristic change in the wavelength
of the scattered photon in units of angstroms? How does this compare
with the Compton wavelength, Ac?
8.
Verify that the units of Planck's
momentum.
9.
A one-electron atom is an atom with Z protons in the nucleus, and
with all hut onC'of its electrons lost to ionization.
constant
are the units of angular
(a)
Starting with Coulomb's law, determine expressions for the orbital radii and energies for a Bohr model of the one-electron atom
with Z protons.
(b)
Find the radius of the ground-state orbit, the ground-state energy,
and the ionization energy of singly ionized helium (He II).
(c)
Repeat part (b) for doubly ionized lithium (Li III).
atom, suppose the hydrogen atorn were held together solely by the
force of gravity. Determine the radius of the ground-state orbit (in
units of A ~UldAU) and the energy of the ground state (in eV).
It \,CaJculate
.
the energies and wavelengths of all possible photons that are
.' emitted when the electron cascades from the n = 3 to the 11, = 1 orbit
of the hydrogen atom.
'If.
Find the shortest wavelength photon emitted by a downward electron
transition in the Lyman, Balmer, and Paschen series. These wavelengths are known as the ser·ies limits. In which regions of the electromagnetic spectrum are these wavelengths found?
12. An electron
in a television set reaches a speed of about 5 x 109 cm
before it hits the screen. 'What is the wavelength of this electron?
S-l