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.)
The average power emitted during the pulse is .
The wavelength of the ruby lasers,
The output pulse last,
As the pulse begins, 60% are in a first excited state and 40% in the ground state.
Consider the known data as below.
Speed of light,
The rate of energy flow in every pulse is called average power.
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 equation of Plank's relation, to get the energy of the photon that is being emitted by the laser. Now, using this value in the power equation considering the criteria of emitted photons, to find the average power of the emitted pulse.
The energy of the photon due to Planck’s relation,
The average power of the emitted pulse is,
At first, the energy of the photon is calculated using the given data in equation (1) as follows:
Now, according to the problem consider the known data due to the absorption of the emitted photons of the Cr ions in the excited state by the ions in the ground state.as below.
The number of atoms in the excited state, and
The number of atoms in the ground state,
Thus, the average power emitted during the pulse is given using equation (2) and, the given data is as follows.
Hence, the value of the average power is .
Label these statements as true or false:
(a) One (and only one) of these sub shells cannot exist: 2p,4f,3d,1p
(b) The number of values of that are allowed depends on l and not on n.
(c) There are four sub shells for n = 4 .
(d) The smallest value of for a given value of l is l + 1 .
(e) All states with l = 0 also have .
(f) There are n sub shells for each value of n .
When electrons bombard a molybdenum target, they produce both continuous and characteristic x-rays as shown in Fig. 40-13. In that figure the kinetic energy of the incident electrons is 35.0 keV. If the accelerating potential is increased to 50.0 keV, (a) what is the value of , and (b) do the wavelengths of the role="math" localid="1661497027757" and lines increase, decrease, or remain the same?
A hydrogen atom in its ground state actually has two possible, closely spaced energy levels because the electron is in the magnetic field of the proton (the nucleus). Accordingly, energy is associated with the orientation of the electron’s magnetic moment relative to , and the electron is said to be either spin up (higher energy) or spin down (lower energy) in that field. If the electron is excited to the higher energy level, it can de-excite by spin-flipping and emitting a photon. The wavelength associated with that photon is 21 cm. (Such a process occurs extensively in the Milky Way galaxy, and reception of the 21 cm radiation by radio telescopes reveals where hydrogen gas lies between stars.) What is the effective magnitude of as experienced by the electron in the ground-state hydrogen atom?
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