Introduction to spectroscopy

Refraction of light

When a ray of light passes from a transparent substance to another transparent substance, but of different density, it undergoes a deviation. This phenomenon is called refraction .

The incident ray, passing from the air to the glass, was deflected towards the normal (normal = perpendicular) to the separation surface of the two media; in the opposite passage the ray was, however, moved away from the normal.

The angle of refraction depends on the density of the transparent substance.

 

Light scattering

When a ray of white light hits a transparent glass prism obliquely, it is decomposed into many rays of light of different colors.

Newton proposed the following interpretation of the phenomenon:

  • White light is actually a mixture of light of different colors.
  • The glass prism does not create the light of different colors, it simply separates the colors already contained in the white light.
  • The color separation is due to the fact that the deviation depends on the wavelength of the incident ray.

The image that can be collected on a screen or photographic film is called a spectrum and shows a series of colors ranging from red to violet .

The spectrum analysis shows how the red radiation ( l = 750 nm ) is deflected less than the violet radiation
( l = 350 nm ).

 

This spectrum is also referred to as a continuous emission spectrum . All incandescent bodies give continuous spectra: solid and liquid.

 

Emission spectra

By breaking down with a glass prism a ray of light coming from a lamp containing the gaseous dopene, we observe the formation of a characteristic spectrum consisting of four distinct lines on a black background. These lines are found two on the violet one on the blue and one on the red .

Changing the gas contained in the lamp also changes the emission spectrum obtained.

In these spectra there is no succession of shaded colors, but only clear, colored lines on a black background.

They are typical of low pressure incandescent gases. The number of lines, their color and their wavelength
( l ) vary as the gas considered varies.

Each gaseous or gaseous element has its own emission spectrum.

Absorption spectra

When a gas or vapor, at a temperature lower than that of the white light source, is interposed between the source itself and the spectroscope, an absorption spectrum is obtained ; it has one or more black ( absorption ) lines on a continuous colored background.

Comparing the emission spectrum to the absorption spectrum of the same substance we see that the black lines in the absorption spectrum fall in the same position ( same l ) as the colored lines of the emission spectrum. The two spectra correspond to their negative like a photo.

It can be concluded affirming that all substances absorb light radiation in the same l unghezza wavelength ( l ) and frequency ( n ) of those which are able to emit. The spectroscopy is a very useful means of chemical-physical analysis of the substances.

 

Interpretation of the emission spectrum of hydrogen
according to the atomic model of Bohr

The regularity of the emission spectrum of an element, that is the fact that it was always formed by the same and characteristic radiations, regardless of its origin and of any excitation procedures to which it had been subjected, could not find any valid explanation with the model proposed by Rutherford in 1911. The first to tackle the problem, on a mathematical basis, was Niels Bohr in 1913.

Bohr accepted the planetary model proposed by Rutherford and, to explain the regularity of behavior of the emission spectrum of hydrogen, introduced some postulates drawn from quantum mechanics .

In the hydrogen atom, the electron moves along preferential circular orbits ( stationary orbits ) each characterized by a certain radius and a certain amount of energy (energy levels ). When the electron travels through these orbits, the H atom does not emit or absorb energy. These orbits were indicated with the letters K, L, M, N, O, P, Q . Each orbit was also associated with a positive integer called quantum number ( K: n = 1 ; L: n = 2 ; M: n = 3 ; etc.). Bohr then determined the radii of the orbits: K: r = 0.052 nm; L: r = 0.212 nm; M: r = 0.477 nm, etc ..

 

In the unexcited atom, the electron travels through the orbit closest to the nucleus ( K orbit ); this orbit is characterized by the minimum energy value, indicated as E 0 (we read: and with zero ), compared to those of the other orbits. To all the other orbits described by the electron, the energies of which increase as one moves away from the nucleus, correspond excited states ( E 1 , E 2 , etc.).

Emission of energy in the form of electromagnetic waves occurs only when an electron jumps from a stationary orbit with higher energy to another with lower energy.
The quantum of energy emitted , D E (read: delta e ) corresponds to the difference between the energy of the stationary state of departure and that of arrival of the electron. For example, if the hydrogen atom is given energy from the outside, the electron jumps from the ground state K , to energy 0 , to the excited state L ( 1) and, without further excitation, it returns to the ground state K ; the energy released is given by the formula D E = E 1 – E 0 , where E 1 indicates the energy of the electron in the L orbit and E 0 the energy in the K orbit.

The frequency ( n ) of the emitted radiation is given by the formula D E = h · n where h is called Plank’s constant, whose value is
6.63 · 10 -34 J s .

The frequency is related to the wavelength ( l ) of the radiation by the formula n = c / l , where c is the speed of light , that is
3.00 · 10 8 m / s
 .

A line of the spectrum corresponds to each electronic transition ( jump ). Since the orbits that can be traveled by the electron are well defined, the possible electronic transitions from one orbit to the previous are limited in number. The energy emitted in the form of electromagnetic radiation is made up of discrete ( discontinuous ) quantities ; the frequencies and wavelengths of the various radiations are also discrete and cover a very small part of the visible spectrum.

The formula with which the potential energy E p is obtained is the following: p = m g h , where:
m = mass in kg,
g = gravitational acceleration force = 9.8 m / s 2 h = height in meters.

From careful spectroscopic studies it appears that the four lines of the visible hydrogen spectrum come from the following electronic transitions:

1 ( red ): radiation with a considerable wavelength and low frequency.

4 ( violet ): radiation with a small wavelength and high frequency.

 

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