X rays with a wavelength of 71 pm are directed onto a gold foil and eject tightly bound electrons from the gold atoms. The ejected electrons then move in circular paths of radius r in a region of the uniform magnetic field . For the fastest of the ejected electrons, the product Br is equal to localid="1664288408568" . Find (a) the maximum kinetic energy of those electrons and (b) the work done in removing them from the gold atoms.
1. The maximum kinetic energy is 3.1 keV.
2. The work done is 14 keV.
The given data is listed below.
The product of B and r is
The wavelength of the X rays is
The kinetic energy of a particle equals the amount of work required to accelerate the particle from rest to speed v. Therefore, kinetic energy on the particle is given by-
The kinetic energy is a scalar, always positive or zero.
The radius is given by
Here, is the mass of the electron, q is the charge of the electron, v is the speed of an electron, and B is the magnetic field.
Now, the speed of an electron can be obtained from equation (1)
Therefore, kinetic energy is given by-
Thus, the maximum kinetic energy of the electrons is 3.1 keV.
Write the equation for energy of photon as below
The Plank’s constant is
The speed of light is,
Therefore, the value of hc is,
Hence, the work done in removing the electrons from gold atoms is 14 keV.
A satellite in Earth orbit maintains a panel of solar cells of area perpendicular to the direction of the Sun’s light rays. The intensity of the light at the panel is . (a) At what rate does solar energy arrive at the panel? (b) At what rate are solar photons absorbed by the panel? Assume that the solar radiation is monochromatic, with a wavelength of 550 nm, and that all the solar radiation striking the panel is absorbed. (c) How long would it take for a “mole of photons” to be absorbed by the panel?
Neutrons in thermal equilibrium with matter have an average kinetic energy of , where is the Boltzmann constant and T, which may be taken to be , is the temperature of the environment of the neutrons. (a) What is the average kinetic energy of such a neutron? (b) What is the corresponding de Broglie wavelength?
X rays of wavelength 0.0100 nm are directed in the positive direction of an axis onto a target containing loosely bound electrons. For Compton scattering from one of those electrons, at an angle of , what are (a) the Compton shift, (b) the corresponding change in photon energy, (c) the kinetic energy of the recoiling electron, and (d) the angle between the positive direction of the axis and the electron’s direction of motion?
94% of StudySmarter users get better grades.Sign up for free