UNIT 2 ( PAGE 3)
ELECTROMAGNETIC SPETCRUM
Various types of electromagnetic radiation having different wave lengths are known. They constitute the electromagnetic spectrum. The arrangement of different types of electromagnetic radiations in the order of increasing wave lengths (or decreasing frequencies) is known as Electromagnetic Spectrum. The complete electromagnetic spectrum is shown in Fig 14.
Electromagnetic spectrum
Different regions of spectrum are identified by different names.
Radiations having wave length from 380 nm to 760 nm are called visible light radiations because our eyes can detect only these radiations. The different colours constituting the visible light are shown in the Figure.
Wave lengths of colours constituting the visible light.
Apart from visible light radiations, some other types of electromagnetic radiations are also known to exist. Radiations having wave length higher than those of red light ( = 760 nm) are called infra red radiations while the radiation with wave length lower than those of violet ( = 380 nm) are known as ultra violet radiations. Some important electromagnetic radiations in the decreasing order of their wave lengths are :
Radio waves > Microwaves > Infrared (IR) > Visible >
Ultra violet (UV) > X-rays > Gamma rays > Cosmic rays
Sources of Electromagnetic Radiations
(i) Radio waves ( 104 Hz) are generated from alternating electric currents of high frequencies. These are used in broadcasting.
(ii) Microwaves ( 1010 Hz) are produced by special generators, e.g. Klystron tube. These are used in telephone transmission and radar. These are also absorbed by food molecules and hence are used to cook food.
(iii) IR radiations ( 1013 Hz) are emitted by incandescent objects. These produce high thermal effect and is heat radiation. These are used in physiotherapy. A plot of the frequencies of IR radiations versus the intensities of radiations absorbed is called infrared spectrum and used to identify a substance because each substance has a characteristic infra-red spectrum.
(iv) Visible light radiations ( 3.95 x 1014 – 7.9 x 1014 Hz) are produced from stars, arc lamps, hot filaments as of tungsten in an electric bulb.
(v) Ultra-violet radiations ( 1016Hz) are present in sun’s rays. In the laboratory these can be produced from the arc lamps containing mercury vapour, xenon or hydrogen gas.
(vi) X-rays ( 1019 Hz) are produced when a stream of electrons strike a heavy metal target. These are used in radiotherapy.
(vii) Cosmic rays ( 3 x 1020 Hz to infinity) originate from the outer space and continously fall on the earth due to their great penetrating power.
Characteristics of electromagnetic radiations
The main characteristics of electromagnetic radiation may be summed up as follows :
i) Electromagnetic radiation propagates through space in
the form of waves. These waves may be described as oscillating electric and magnetic fields which are perpendicular to each other.
ii) All the electromagnetic radiation travel with the velocity
of light.
iii) These radiation do not require any medium for transmission.
iv) The energy of an electromagnetic radiation is directly proportional to its frequency or inversely proportional to its wave length.
PARTICLE NATURE OF ELECTROMAGNETIC RADIATION - PLANCK’S QUANTUM THEORY
Some of the experimental phenomena such as diffraction and interference can be explained by the wave nature of the electromagnetic radiation. However, experimental observations such as emission of radiation from a hot body and photoelectric effect cannot be explained on this basis.
When solids are heated they emit radiation over a wide range of wave lengths. For example, when an iron rod is heated in a furnace, it first turns a dull red and then progressively becomes more and more red as temperature increases. As this is heated further, the radiation emitted becomes white and then becomes blue as temperature becomes very high. In terms of frequency, it means that the radiation emitted goes on from a lower frequency to a higher frequency as the temperature increases. The red colour lies in the lower frequency region , while blue colour belongs to the higher frequency region of the electromagnetic spectrum. The ideal body , which emits and absorbs all frequencies, is called black body and the radiation emitted by this body is called black body radiation. The exact frequency distribution of the emitted radiation (i.e., intensity versus frequency curve of the radiation ) from a black body depends upon its temperature. At a given temperature, intensity of radiation emitted increases with decrease of wave length, reaches a maximum value at a given wave length and then starts decreasing with further decrease of wave length, as shown in Fig.
Wave length – intensity relationship
The above experimental results cannot be explained on the basis of the wave theory of light. In 1900 , Max Planck provided an explanation for this behaviour. He said that atoms and molecules could emit (or absorb) energy only in discrete quantities . Planck gave the name quantum to the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. The energy of a quantum of radiation is proportional to its frequency and is expressed as :
E
E = h
The proportionality constant, h , is known as Planck constant and has the value 6.626 x 1034 J s
According to Planck’s theory, energy is always emitted in integral multiples of h , for example h , 2 h , 3 h etc. Planck however, could not explain why energies should be quantised in this manner. However, with this assumption, Planck could explain the distribution of intensity in radiation from black body as a function of frequency at different temperatures.
PHOTOELECTRIC EFFECT
Experiments show that electrons are ejected from the surface of certain metals( like Cs, K and Rb) when they are exposed to light of appropriate frequency. This phenomenon is known as photoelectric effect.
Equipment for studying the photoelectric effect.
Light of a particular frequency strikes a clean metal surface inside a vaccum chamber. Electrons are ejected from the metal and are counted by a detector that measures their kinetic energy.
According to the wave theory of light , both the number of electrons ejected and their energies should depend upon the intensity of the incident light. In practice, it is found that , while the number of electrons ejected does depend on the intensity of the incident light, their energies do not. Einstein was able to explain the photoelectric effect by making the most extraordinary assumption. He suggested that light consists of stream of particles called photons which move with the speed of light. Using Planck’s quantum theory of radiation, Einstein deduced that each photon must possess energy E, given by E = h where is the frequency of light.
Shooting beam of light onto a metal surface can, therefore , be viewed as shooting beam of particles – the photons. When a photon strikes an electron in the atom of the metal with sufficient energy, the electron may be knocked out of the atom. The more energetic the photon is, the more energy it transfers to the electron and the greater the energy of the ejected electron. A more intense beam of light consists of a large number of photons, consequently the number of electrons ejected is also larger as compared to an experiment in which a beam of weaker intensity of light is employed.
Threshold frequency (o) and kinetic energy of photoelectrons
For each metal , there is a characteristic minimum frequency – the threshold frequency (o) – below which the photoelectric effect does not occur. Red light ( = 4.3 – 4.6 x 1014 Hz) , for example, of any intensity may shine on a piece of potassium for hours but no photoelectrons will be released. But as soon as even very weak yellow light (= 5.1 – 5.2 x 1014 Hz) shines on potassium , the photoelectric effect is observed. The threshold frequency , o for potassium is 5 x 1014 Hz. For photoelectric effect to occur, the striking photon should have frequency more than that of the threshold frequency. If a photon of frequency () strikes a metal atom whose threshold frequency o , then photoelectrons will be emitted only if > o . Since the striking photon has energy equal to h and the minimum energy required to eject electron is ho (also called work function, Wo), then h ho is transformed as the kinetic energy of the photoelectron ( ½ mv2) where m is the mass of electron and v is its velocity. Since the total energy has to be conserved, one way to write Einstein’s equation as
h ho = ½ mv2 = kinetic energy of electron
DUAL NATURE OF ELECTROMAGNETIC RADIATIONS
Einstein (1905 ) proposed that light is propagated in the form of small packets of energy called photons. These photons can be treated as particles of light. Certain phenomena such as Photoelectric Effect and Black body Radiation can be explained only on the basis of particle nature of light. On the other hand , light also exhibits phenomena of interference and diffraction which indicated that light also has wave character. Thus light has dual character , i.e., particle as well as wave character.
Problems
1. Calculate the number of protons, neutrons and electrons in 8035Br.
2. The number of electrons, protons and neutrons in a species are equal to 18, 16 and 16 respectively. Assign proper symbol to the species.
3. The Vividh Bharathi station of All India Radio, Delhi broadcasts on a frequency of 1,368 kHz. Calculate the wave length of the electromagnetic radiation emitted by the transmitter. Which part of the electromagnetic spectrum does it belong ?
4. The wave length range of the visible spectrum extends from violet (400 nm ) to red (750 nm ) . Express the wave lengths in frequencies (Hz).
5. One of the spectral lines of caesium has a wave length of 456 nm. Calculate the frequency of this line.
6. The frequency of the strong yellow line in the spectrum of sodium is 5.09 x 1014 s1. calculate the wave length of this light in nanometres.
7. Calculate the frequency of light of wave length 4000 A.
8. A visible radiation has a frequency of 6 x 1014 cycles s1. Find out the wave length of the radiation in nanometres.
9. Calculate (a) wave number and (b) frequency of yellow radiation having wave length 5800 A.
10. Calculate the energy of one mole of photons of radiation whose frequency is 5 x 1014 Hz.
11. Calculate the total number of electrons present in one mole of methane.
12. Find (a) total number and (b) the total mass of neutrons in 7 mg of 14C
(assume that mass of a neutron = 1.675 x 1027 kg)
13. Find (a) the total number and total mass of protons in 34 mg of NH3 at STP.
14. A 100 watt bulb emits monochromatic light of wave length 400 nm. Calculate the number of photons emitted per second by the bulb.
15. Yellow light emitted from a sodium lamp has a wave length () of 580 nm. Calculate its frequency() and wave number() of yellow light.
16. Find energy of each of the photons which :
(i) Correspond to light of frequency 3 x 1015 Hz.
(ii) have wave length of 0.05 A.
17. The threshold frequency o of the metal is 7.0 x 1014 Hz. Calculate the kinetic energy of an electron emitted when radiation of frequency = 1 x 1015 Hz hits the metal.
18. Calculate the wave length, frequency and wave number of light wave whose period is 2.0 x 1010 s.
19. What is the number of photons of light with wave length of 4000 pm that provide 1 J of energy ?
20. A photon of wave length 4 x 107 m strikes on metal surface , the work function of the metal being 2.13 eV.
Calculate :
(i) the energy of photon (eV) ,
(ii) the kinetic energy of the emission, and
(iii) the velocity of the photoelectron ( 1 eV = 1.6020 x 1019 J).
21. Electromagnetic radiation of wave length 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in kJ mol1 .
22. A 25 watt bulb emits monochromatic yellow light of wave length of 0.57 m. Calculate the rate of emission of quanta per second.
23. Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wave length 6800 A. Calculate threshold frequency(o) of metal.
24. What is the wave length of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n = 4 to an energy level with n = 2 ?
25. How much energy is required to ionise a H atom if the electron occupies n = 5 orbit ? Compare your answer with ionisation enthalpy of H atom (energy required to remove the electron from n = 1 orbit).
26. What is the maximum number of emission lines when the excited electron of a H atom in n = 6 drops to the ground state ?
27. The energy associated with first orbit in hydrogen atom is 2.18 x 1018 J atom1. What is the energy associated with the fifth orbit ?
28. Calculate the radius of Bohr’s fifth orbit for hydrogen atom.
29. Calculate the wave number for the longest wave length transition in Balmer series of atomic hydrogen.
30. When electromagnetic radiation of wave length 300 nm falls on the surface of sodium electrons are emitted with a kinetic energy of 1.68 x 105 J mol1. What is the minimum energy needed to remove an electron from sodium ? What is the maximum wave length that will cause a photoelectron to be emitted .
Solar Spectrum
When white light from the sun is passed through a prism, it splits up into a series of colour bands known as rainbow of colours ; Violet, Indigo, Blue, Green, Yellow , Orange and Red (VIBGYOR). This means that sunlight is composed of collection of electromagnetic waves having different wave lengths. The prism bends the light of different wavelengths
Fig 16. Solar spectrum.
to different extends. The splitting of light into seven colours is known as Dispersion and the series of colour bands is called Spectrum. In this spectrum, there is continuity of colours i.e., one colour merges into the other without any gap or discontinuity and such spectrum is known as Continuous spectrum. The continuous spectrum can also be obtained from the light emitted from incandescent substances.
Atomic Spectra ( Line spectra)
When gases or vapours of chemical substances are heated by electric spark , light is emitted. The colour of the light depends upon the substance under investigation. For example, sodium or salt of sodium gives yellow light, while potassium or salt of potassium produces violet colour. Such colours can be studied by an instrument called spectroscope. When radiation emitted by different substances are analysed , the spectrum obtained consists of sharp well defined lines of definite frequency. Such a spectrum consisting of lines of definite frequencies is called Line Spectrum or Discontinuous spectrum.
An electric spark is passed through hydrogen gas in a discharge tube. The light emitted by hydrogen atoms is formed into a narrow beam and passed through a prism which divides the beam into several beams that form the line spectrum when they strike the screen. The four lines whose wave lengths are listed are those that can be seen in the visible portion of hydrogen spectrum.
Fig 17. The emission spectrum of hydrogen atom.
The line spectrum is also known as atomic spectrum because it is obtained by analysing the emitted radiation from the atoms by the application of heat or other forms of energy. This is known as Emission Spectrum of a particular atom or molecule because it is obtained by analysing the emitted radiation. The pattern of lines in the spectrum of the element is characteristic of that element and is different from those of all other elements. In other words each element gives a unique spectrum irrespective of even the form in which it is present.
For example, the lines at 589 nm and 589.6 nm are the important lines in the spectrum of sodium, whatever may be its source. It is for this reason, that the line spectra are also regarded as finger print of atoms.
Since atoms of different elements give characteristic set of lines of definite frequencies, emission spectrum can be used in chemical analysis to identify and estimate the elements present in a sample. The elements Rubedium and caesium were discovered by this way. When a continuous electromagnetic radiation ( say white light ) is allowed to pass through a gas or through a solution of some salt and transmitted light is analysed , we obtain spectrum in which dark lines are observed in an otherwise continuous spectrum. These dark lines indicate that the radiation of corresponding wave lengths have been absorbed by the substance from white light. Such a spectrum containing a few dark lines due to the absorption of light is known as Absorption spectrum.
Fig. 18 . Absorption spectrum of sodium chloride.
Spectrum of Hydrogen
The spectrum of hydrogen atom can be obtained by passing an electric discharge through the gas taken in the discharge tube under low pressure. The emitted light is analysed with the help of a spectroscope. The spectrum consists of a large number of lines appearing in different regions of wave lengths. Some of the lines are present in the visible region while others in Ultra violet and infra red regions.
In 1885 J.J. Balmer developed a simple relationship among the different wave lengths of the series of visible lines in the hydrogen spectrum. The relationship is :
where ‘n’ is an integer equal to or greater than 3
( i.e., 3, 4, 5 ......).
The Balmer formula give only the spectral lines which appear in the visible region is named as Balmer Series. Soon afterwards , a series of spectral lines of hydrogen atom in different regions were grouped into five different series of lines, each named after the names of their discoverer. They are Lyman series, Balmer series, Paschen series , Brackett series and Pfund series. Lyman series appear in the ultra-violet region, Balmer series appear in the visible region, while the other series appear in the infra-red region.
As the other series of hydrogen spectral lines were discovered a more general expression was found as :
where n1 and n2 are integers , such that n1 n2 . R is called Rydberg Constant. The value of R is 10967800 m1. The equation is valid for all lines in the hydrogen spectrum and is known as Rydberg equation. The Complete spectrum of hydrogen atom is shown below: :
Complete atomic spectrum of hydrogen
For a given series n1 remains constant while n2 varies from line to line in the same series. For example, for Lyman series n1 = 1 and n2 = 2, 3, 4, 5......and for Balmer series n1 = 2 and n2 = 3, 4, 5, ...... All the five series , the regions in which the lines appear and the various values of n1 and n2 are given below.
Series | Region | n1 | n2 |
Lyman | Ultra violet | 1 | 2,3,4,.… |
Balmer | Visible | 2 | 3,4,5,.… |
Paschen | Infrared | 3 | 4,5,6,.… |
Brackett | Infrared | 4 | 5,6,7,.… |
Pfund | Infrared | 5 | 6,7,8,…. |
The Rydberg equation is applicable for spectral lines of hydrogen atom. The spectrum of other atoms are complex , consisting of large number of lines whose wave lengths cannot be related by a simple relation as Rydberg Equation.