When photons pass through matter, the intensity I of the beam (measured in watts per square meter) decreases exponentially according to I = I0e-μxwhere I is the intensity of the beam that just passed through a thickness x of material and I0 is the intensity of the incident beam. The constant μ is known as the linear absorption coefficient, and its value depends on the absorbing material and the wavelength of the photon beam. This wavelength (or energy) dependence allows us to filter out unwanted wavelengths from a broad-spectrum x-ray beam.(a) Two x-ray beams of wavelengths λ1 and λ2 and equal incident intensities pass through the same metal plate. Show that the ratio of the emergent beam intensities is (I2)/(I1) = e-(μ2 - μ1)x(b) Compute the ratio of intensities emerging from an aluminum plate 1.00 mm thick if the incident beam contains equal intensities of 50 pm and 100 pm x-rays. The values of μ for aluminum at these two wavelengths are μ1 = 5.40 cm-1 at 50 pm and μ2 = 41.0 cm-1 at 100 pm. (c) Repeat part (b)for an aluminum plate 10.0 mm thick.
Atomic Spectra
According to the Bohr model of an atom, the electron in an atom moves around a nucleus in fixed orbits with specific energies known as energy levels. The orbital energies are quantized. The electrons remain in these energy levels until they emit or absorb a photon of a particular wavelength, the quantum of energy. If the electron emits a photon, it then falls back to a lower energy level, and if it absorbs a photon, the electron rises to higher energy levels. The photons released or absorbed in these transitions of an electron are studied and analyzed on a screen as atomic spectra.
Ruby Lasers
Lasers are devices that emit light using atoms or molecules at a certain wavelength and amplify the light to produce a narrow beam of radiation. It works as per the principle of electromagnetic radiation. Their source of emission contains the same frequency and same phase. It was invented in the year 1960 by the great noble scientist, Theodore Maiman.
Balmer Series
The spectrum of frequency observed when electromagnetic radiation is emitted from an atom when it goes from higher energy state to lower state, is known as emission spectrum. This transition occurs when an excited electron moves from higher to lower state. It has many possible electron transitions and each transition has a specific energy difference.
Emission Spectrum
Every state of matter tries to be at minimum potential energy or it can be said that the atoms of element/ substance arrange themselves such that overall energy is minimum.
When photons pass through matter, the intensity I of the beam (measured in watts per square meter) decreases exponentially according to
I = I0e-μx
where I is the intensity of the beam that just passed through a thickness x of material and I0 is the intensity of the incident beam. The constant μ is known as the linear absorption coefficient, and its value depends on the absorbing material and the wavelength of the photon beam. This wavelength (or energy) dependence allows us to filter out unwanted wavelengths from a broad-spectrum x-ray beam.
(a) Two x-ray beams of wavelengths λ1 and λ2 and equal incident intensities pass through the same metal plate. Show that the ratio of the emergent beam intensities is
(I2)/(I1) = e-(μ2 - μ1)x
(b) Compute the ratio of intensities emerging from an aluminum plate 1.00 mm thick if the incident beam contains equal intensities of 50 pm and 100 pm x-rays. The values of μ for aluminum at these two wavelengths are μ1 = 5.40 cm-1 at 50 pm and μ2 = 41.0 cm-1 at 100 pm. (c) Repeat part (b)
for an aluminum plate 10.0 mm thick.
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