BackA ruby laser emits an intense pulse of light that lasts a mere 10 ns. The light has a wavelength of 690 nm, and each pulse has an energy of 500 mJ. What is the rate of photon emission, in photons per second, during the 10 ns that the laser is 'on'?
The graph in FIGURE P38.42 was measured in a photoelectric-effect experiment. What is the work function (in eV) of the cathode?
A beam of alpha particles is incident on a target of lead. A particular alpha particle comes in 'head-on' to a particular lead nucleus and stops m away from the center of the nucleus. (This point is well outside the nucleus.) Assume that the lead nucleus, which has protons, remains at rest. The mass of the alpha particle is kg.
(a) Calculate the electrostatic potential energy at the instant that the alpha particle stops. Express your result in joules and in MeV.
(b) What initial kinetic energy (in joules and in MeV) did the alpha particle have?
(c) What was the initial speed of the alpha particle?
A -MeV alpha particle from a Ra decay makes a head-on collision with a uranium nucleus. A uranium nucleus has protons.
(a) What is the distance of closest approach of the alpha particle to the center of the nucleus? Assume that the uranium nucleus remains at rest and that the distance of closest approach is much greater than the radius of the uranium nucleus.
(b) What is the force on the alpha particle at the instant when it is at the distance of closest approach?
Through what potential difference must electrons be accelerated if they are to have:
(a) the same wavelength as an x ray of wavelength nm; and
(b) the same energy as the x ray in part (a)?
Calculate the de Broglie wavelength of a -g bullet that is moving at m/s. Will the bullet exhibit wavelike properties?
An electron is moving with a speed of m/s. What is the speed of a proton that has the same de Broglie wavelength as this electron?
An alpha particle ( kg) emitted in the radioactive decay of uranium- has an energy of MeV. What is its de Broglie wavelength?
An electron has a de Broglie wavelength of m. Determine (a) the magnitude of its momentum and (b) its kinetic energy (in joules and in electron volts).
For crystal diffraction experiments (discussed in Section ), wavelengths on the order of nm are often appropriate. Find the energy in electron volts for a particle with this wavelength if the particle is a photon.
(a) An electron moves with a speed of m/s. What is its de Broglie wavelength?
(b) A proton moves with the same speed. Determine its de Broglie wavelength.
(a) The -coordinate of an electron is measured with an uncertainty of mm. What is the x-component of the electron's velocity, , if the minimum percent uncertainty in a simultaneous measurement of is ?
(b) Repeat part (a) for a proton.
A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of nm and its momentum component along this axis with a standard deviation of kg-m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claim.
The uncertainty in the y-component of a proton's position is m. What is the minimum uncertainty in a simultaneous measurement of the -component of the proton's velocity?
A pesky -mg mosquito is annoying you as you attempt to study physics in your room, which is m wide and m high. You decide to swat the bothersome insect as it flies toward you, but you need to estimate its speed to make a successful hit.
(a) What is the maximum uncertainty in the horizontal position of the mosquito?
(b) What limit does the Heisenberg uncertainty principle place on your ability to know the horizontal velocity of this mosquito? Is this limitation a serious impediment to your attempt to swat it?