Show that the cutoff wavelength in the continuous x-ray spectrum from any target is given by , where is the potential difference (in kilovolts) through which the electrons are accelerated before they strike the target.
It is shown that the cutoff wavelength in the continuous x-ray spectrum from any target is given by .
A continuous x-ray spectrum from any target is produced due to the striking of the electrons that are accelerating before the strike.
Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the magnetic frequency of the photon and thus, equally, equates to the wavelength of the wave. When the frequency of photons is high, its potential is high.
Using the energy relation of Planck's equation and the energy difference created by the accelerating electron due to generated potential difference, to get the required equation of the cutoff wavelength in the continuous x-ray spectrum from any target.
The energy of the photon due to Planck’s relation,
Consider the known data below.
The Plank’s constant is,
The speed of light is,
The energy generated due to accelerating potential,
Here, e is the charge and V is the potential.
As the accelerating electrons strike the target, they generate the same energy difference on the target as due to the accelerating potential. Thus, using equations (1) and (2), the cutoff wavelength in the continuous x-ray spectrum from any target is given by:
Here, the potential V is in the kilovolts.
Hence, it is proved that the wavelength value is .
Ruby lasers are at a wavelength of 694 nm. A certain ruby crystal has Cr ions (which are the atoms that lase). The lasing transition is between the first excited state and the ground state, and the output is a light pulse lasting . As the pulse begins, 60.0% of the Cr ions are in the first excited state and the rest are in the ground state. What is the average power emitted during the pulse? (Hint: Don’t just ignore the ground-state ions.)
Figure 40-25 is an energy-level diagram for a fictitious three-dimensional infinite potential well that contains one electron. The numbers of degenerate states of the levels are indicated: “non” means non-degenerate (which includes the ground state) and “triple” means 3 states. If we put a total of 22 electrons in the well, what multiple of gives the energy of the ground state of the 22 electron system? Assume that the electrostatic forces between the electrons are negligible.
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