[Physics] Wavelength vs Intensity graph for X-rays


Why is the nature of graph like that? I mean intensity if proportional to energy which is equivalent to $hc /\lambda $ . So, by this we should get a hyperbola. But why do we see that the graph reaches a maximum value and then again decreases?
The graph is something like this –
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What about this? enter image description here

Best Answer

When we produce X rays in a CRT, we find 2 sources for the shape of the graph : 1. Characteristic X-rays, and 2. Brehmsstrahlung X-rays (braking radiation, the continuum part of the spectrum)

  1. Characteristic X-rays

These occur in situations where an electron undergoes a direct "head on" interaction with a valence shell electron of an atom in the anode, ionizes the atom, and that electron is given enough momentum to send it off as a free particle. Nearby electrons fill the vacancy, emitting energy as photons and this energy appears as radiative energy.

The discrete nature of the energy levels results in "spikes" in the specturm at certain frequencies, as the energy gaps between shells are quantized (i.e have fixed set of values), the energy of resulting X-rays, too have fixed energy. They're called "characteristic x-rays".

  1. Brehmsstrahlung X-rays (braking radiation, the continuum part of the spectrum)

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Bremsstrahlung produced by a high-energy electron deflected in the electric field of an atomic nucleus.

Interactions between incoming electrons and anode atoms can obviously occur in many ways. If an interaction does not produce a ionisation , due to lack of momentum, the incoming electrons can produce many different interactions resulting in minor to major energy changes, that is the continuous spectrum.

Bremsstrahlung (German pronunciation: [ˈbʁɛmsˌʃtʁaːlʊŋ], from bremsen "to brake" and Strahlung"radiation"; i.e., "braking radiation" or "deceleration radiation") is electromagnetic radiationproduced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon, thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.

Broadly speaking, Bremsstrahlung or braking radiation is any radiation produced due to the deceleration (negative acceleration) of a charged particle, which includes synchrotron radiation,cyclotron radiation, and the emission of electrons and positrons during beta decay. However, the term is frequently used in the more narrow sense of radiation from electrons (from whatever source) slowing in matter.

Bremsstrahlung emitted from plasma is sometimes referred to as free/free radiation. This refers to the fact that the radiation in this case is created by charged particles that are free; i.e., not part of an ion, atom or molecule, both before and after the deflection (acceleration) that caused the emission.

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Spectrum of the X-rays emitted by an X-ray tube with a rhodium target, operated at 60 kV. The continuous curve is due to bremsstrahlung, and the spikes are characteristic K lines for rhodium.

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