67. * (a) Calculate the electric potential difference needed to accel- erate a proton so that it has a wavelength of 1.0 × 10-12 m. (b) Repeat the calculation for an electron. Hint: Here you must use the relativistic expressions for energy and momentum. (c) Compare the energies of these two particles (ratio of energy to electron energy) when they have this same wavelength. proton

67. * (a) Calculate the electric potential difference needed to accel- erate a proton so that it has a wavelength of 1.0 × 10-12 m. (b) Repeat the calculation for an electron. Hint: Here you must use the relativistic expressions for energy and momentum. (c) Compare the energies of these two particles (ratio of energy to electron energy) when they have this same wavelength. proton

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter28: Atomic Physics

Section: Chapter Questions

Problem 5P

See similar textbooks

Similar questions

Construct Your Own Problem Consider an ultrahighenergy cosmic ray entering the Earth’s atmosphere (some have energies approaching a joule). Construct a problem in which you calculate the energy of the particle based on the number of particles in an observed cosmic ray shower. Among the things to consider are the average mass of the shower particles, the average number per square meter, and the extent (number of square meters covered) of the shower. Express the energy in eV and joules.
The velocity of a proton emerging from a Van de Graaff accelerator is 25.0% of the speed of light. (a) What is the proton's wavelength? (b) What is its kinetic energy, assuming it is nonrelativistic? (c) What was the equivalent voltage through which it was accelerated?
(a) The lifetime of a highly unstable nucleus is 10-20. What is the smallest uncertainty in its decay energy? (b) Compare this with the rest energy of an electron.
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 45.0°C assuming a specific heat of 0.900kcal/kgC ? Neglect all other heat transfer. (c) How long must the microwave operator wait for their pasta to be ready?
Integrated Concepts In a Millikan oil-drop experiment using a setup like that in Figure 30.9, a 500-V potential difference is applied to plates separated by 2.50 cm. (a) What is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates? (b) What is the diameter of the drop, assuming it is a sphere with the density of olive oil?
(a) Calculate the wavelength of a photon that has the same momentum as a proton moving at 1.00% of the speed of light. (b) What is the energy of the photon in MeV? (c) What is the kinetic energy of the proton in MeV?
What is the maximum velocity of electrons ejected from a material by 80-nm photons, if they are bound to the material by 4.73 eV?
An atom can be formed when a negative muon is captured by a proton. The muon has the same charge as the electron and a mass 207 times that of the electron. Calculate the frequency of the photon emitted when this atom makes the transition from n=2 to the n=1 state. Assume that the muon is orbiting a stationary proton.
(a) Find the momentum of a 100-keV x-ray photon. (b) Find the equivalent velocity of a neutron with the same momentum. (c) What is the neutron's kinetic energy in keV?
Integrated Concepts Sunlight above the Earth's atmosphere has an intensity of 1.30kW/m2. 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?
Construct Your Own Problem Consider a highly relativistic particle. Discuss what is meant by the term "highly relativistic." (Note that, in part, it means that the particle cannot be massless.) Construct a problem in which you calculate the wavelength of such a particle and show that it is very nearly the same as the wavelength of a massless particle, such as a photon, with the same energy. Among the things to be considered are the rest energy of the particle (it should be a known particle) and its total energy, which should be large compared to its rest energy.
Integrated Concepts (a) An excimer laser used for vision correction emits 193-nm UV. Calculate the photon energy in eV. (b) These photons are used to evaporate corneal tissue, which is very similar to water in its properties. Calculate the amount of energy needed per molecule of water to make the phase change from liquid to gas. That is, divide the heat of vaporization in kJ/kg by the number of water molecules in a kilogram. (c) Convert this to eV and compare to the photon energy. Discuss the implications.