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?
The effective magnitude of magnetic field as experienced by the electron in the ground-state hydrogen atom is 51 mT .
Magnetic resonance, absorption or radiation by electrons or atomic nuclei in response to the use of other magnetic fields.
The power of attraction among all the crowds throughout the universe; especially the attraction of the gravity of the earth with the bodies near its surface.
Use the concept of gravitational force to find gravitational potential energy. Integrate the equation of gravitational force over infinity to reference position. Then define the work required to increase the separation of the particles for the given positions.
The energy equation from the Stern-Gerlach experiment,
Here, B is the magnetic field and is the Bohr magneton.
The energy due to Planck-Einstein relation,
Here, c is the speed of light, is the wavelength, and h is the Plank’s constant.
Consider the known data as below.
Speed of light,
Comparing equations (1) and (2) and substituting the given data in the derived equation of the magnetic field.
The value of the effective magnetic field is as follow.
Substitute known values in the above equation.
Hence, the value of the magnetic field is 51 mT.
The active medium in a particular laser generates laser light at a wavelength of 694nm is 6.00 cm long and 1.00 cm in diameter. (a) Treat the medium as an optical resonance cavity analogous to a closed organ pipe. How many standing-wave nodes are there along the laser axis? (b) By what amount would the beam frequency have to shift to increase this number by one? (c) Show that is just the inverse of the travel time of laser light for one round trip back and forth along the laser axis. (d) What is the corresponding fractional frequency shift ? The appropriate index of refraction of the lasing medium (a ruby crystal) is 1.75.
Martian laser. Where sunlight shines on the atmosphere of Mars, carbon dioxide molecules at an altitude of about 75 km undergo natural laser action. The energy levels involved in the action are shown in Fig. 40-26; population inversion occurs between energy levels and . (a) What wavelength of sunlight excites the molecules in the lasing action? (b) At what wavelength does lasing occur? (c) In what region of the electromagnetic spectrum do the excitation and lasing wavelengths lie?
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