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Integrated Concepts
The 54.0-eV electron in [link] has a 0.167-nm wavelength. If such electrons are passed through a double slit and have their first maximum at an angle of $\text{25}\text{.}\mathrm{0\xba}$ , what is the slit separation $d$ ?
0.395 nm
Integrated Concepts
An electron microscope produces electrons with a 2.00-pm wavelength. If these are passed through a 1.00-nm single slit, at what angle will the first diffraction minimum be found?
Integrated Concepts
A certain heat lamp emits 200 W of mostly IR radiation averaging 1500 nm in wavelength. (a) What is the average photon energy in joules? (b) How many of these photons are required to increase the temperature of a person’s shoulder by $2\text{.}\mathrm{0\xba}\text{C}$ , assuming the affected mass is 4.0 kg with a specific heat of $0\text{.83 kcal}\text{/kg}\cdot \text{\xbaC}$ . Also assume no other significant heat transfer. (c) How long does this take?
(a) $1.3\times {\text{10}}^{-\text{19}}\phantom{\rule{0.25em}{0ex}}\text{J}$
(b) $2\text{.}1\times {\text{10}}^{\text{23}}$
(c) $1\text{.}4\times {\text{10}}^{2}\phantom{\rule{0.25em}{0ex}}\text{s}$
Integrated Concepts
On its high power setting, a microwave oven produces 900 W of 2560 MHz microwaves. (a) How many photons per second is this? (b) How many photons are required to increase the temperature of a 0.500-kg mass of pasta by $\text{45}\text{.}\mathrm{0\xba}\text{C}$ , assuming a specific heat of $0\text{.}\text{900 kcal/kg}\cdot \text{\xbaC}$ ? Neglect all other heat transfer. (c) How long must the microwave operator wait for their pasta to be ready?
Integrated Concepts
(a) Calculate the amount of microwave energy in joules needed to raise the temperature of 1.00 kg of soup from $\text{20}\text{.}\mathrm{0\xba}\text{C}$ to $\text{100}\text{\xbaC}$ . (b) What is the total momentum of all the microwave photons it takes to do this? (c) Calculate the velocity of a 1.00-kg mass with the same momentum. (d) What is the kinetic energy of this mass?
(a) $3\text{.}\text{35}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{J}$
(b) $1\text{.}\text{12}\times {\text{10}}^{\text{\u20133}}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}$
(c) $1\text{.}\text{12}\times {\text{10}}^{\text{\u20133}}\phantom{\rule{0.25em}{0ex}}\text{m/s}$
(d) $6.23\times {\text{10}}^{\text{\u20137}}\phantom{\rule{0.25em}{0ex}}\text{J}$
Integrated Concepts
(a) What is $\gamma $ for an electron emerging from the Stanford Linear Accelerator with a total energy of 50.0 GeV? (b) Find its momentum. (c) What is the electron’s wavelength?
Integrated Concepts
(a) What is $\gamma $ for a proton having an energy of 1.00 TeV, produced by the Fermilab accelerator? (b) Find its momentum. (c) What is the proton’s wavelength?
(a) $1\text{.}\text{06}\times {\text{10}}^{3}$
(b) $5\text{.}\text{33}\times {\text{10}}^{-\text{16}}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}$
(c) $1\text{.}\text{24}\times {\text{10}}^{-\text{18}}\phantom{\rule{0.25em}{0ex}}\text{m}$
Integrated Concepts
An electron microscope passes 1.00-pm-wavelength electrons through a circular aperture $2\text{.}\text{00 \mu m}$ in diameter. What is the angle between two just-resolvable point sources for this microscope?
Integrated Concepts
(a) Calculate the velocity of electrons that form the same pattern as 450-nm light when passed through a double slit. (b) Calculate the kinetic energy of each and compare them. (c) Would either be easier to generate than the other? Explain.
(a) $1\text{.}\text{62}\times {\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$
(b) $4\text{.}\text{42}\times {\text{10}}^{-\text{19}}\phantom{\rule{0.25em}{0ex}}\text{J}$ for photon, $1\text{.}\text{19}\times {\text{10}}^{-\text{24}}\phantom{\rule{0.25em}{0ex}}\text{J}$ for electron, photon energy is $3\text{.}\text{71}\times {\text{10}}^{5}$ times greater
(c) The light is easier to make because 450-nm light is blue light and therefore easy to make. Creating electrons with $\mathrm{7.43\; \mu eV}$ of energy would not be difficult, but would require a vacuum.
Integrated Concepts
(a) What is the separation between double slits that produces a second-order minimum at $\text{45}\text{.}\mathrm{0\xba}$ for 650-nm light? (b) What slit separation is needed to produce the same pattern for 1.00-keV protons.
(a) $2\text{.}\text{30}\times {\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{m}$
(b) $3\text{.}\text{20}\times {\text{10}}^{-\text{12}}\phantom{\rule{0.25em}{0ex}}\text{m}$
Integrated Concepts
A laser with a power output of 2.00 mW at a wavelength of 400 nm is projected onto calcium metal. (a) How many electrons per second are ejected? (b) What power is carried away by the electrons, given that the binding energy is 2.71 eV? (c) Calculate the current of ejected electrons. (d) If the photoelectric material is electrically insulated and acts like a 2.00-pF capacitor, how long will current flow before the capacitor voltage stops it?
Integrated Concepts
One problem with x rays is that they are not sensed. Calculate the temperature increase of a researcher exposed in a few seconds to a nearly fatal accidental dose of x rays under the following conditions. The energy of the x-ray photons is 200 keV, and $4\text{.}\text{00}\times {\text{10}}^{\text{13}}$ of them are absorbed per kilogram of tissue, the specific heat of which is $0\text{.}\text{830 kcal/kg}\cdot \text{\xbaC}$ . (Note that medical diagnostic x-ray machines cannot produce an intensity this great.)
$3\text{.}\text{69}\times {\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\mathrm{\xbaC}$
Integrated Concepts
A 1.00-fm photon has a wavelength short enough to detect some information about nuclei. (a) What is the photon momentum? (b) What is its energy in joules and MeV? (c) What is the (relativistic) velocity of an electron with the same momentum? (d) Calculate the electron’s kinetic energy.
Integrated Concepts
The momentum of light is exactly reversed when reflected straight back from a mirror, assuming negligible recoil of the mirror. Thus the change in momentum is twice the photon momentum. Suppose light of intensity $1\text{.}{\text{00 kW/m}}^{2}$ reflects from a mirror of area $2\text{.}{\text{00 m}}^{2}$ . (a) Calculate the energy reflected in 1.00 s. (b) What is the momentum imparted to the mirror? (c) Using the most general form of Newton’s second law, what is the force on the mirror? (d) Does the assumption of no mirror recoil seem reasonable?
(a) 2.00 kJ
(b) $1\text{.}\text{33}\times {\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}$
(c) $1\text{.}\text{33}\times {\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{N}$
(d) yes
Integrated Concepts
Sunlight above the Earth’s atmosphere has an intensity of $1\text{.}\text{30}\phantom{\rule{0.25em}{0ex}}{\text{kW/m}}^{2}$ . If this is reflected straight back from a mirror that has only a small recoil, the light’s momentum is exactly reversed, giving the mirror twice the incident momentum. (a) Calculate the force per square meter of mirror. (b) Very low mass mirrors can be constructed in the near weightlessness of space, and attached to a spaceship to sail it. Once done, the average mass per square meter of the spaceship is 0.100 kg. Find the acceleration of the spaceship if all other forces are balanced. (c) How fast is it moving 24 hours later?
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