ATOMIC SPECTRUM OF HYDROGEN

ATOMIC SPECTRUM OF HYDROGEN

The emission line spectrum

 of hydrogen can be obtained by passing electric discharge through

the gas contained in a discharge tube at low pressure. The light radiation emitted is then examined

with the help of a spectroscope. The bright lines recorded on the photographic plate constitute the

atomic spectrum of hydrogen 

In 1884 J.J. Balmer observed that there were four prominent coloured lines in the visible hydrogen

spectrum :

(1) a red line with a wavelength of 6563 Å.

(2) a blue-green line with a wavelength 4861 Å.

(3) a blue line with a wavelength 4340 Å.

(4) a violet line with a wavelength 4102 Å.

Hydrogen

discharge tube

The examination of the atomic spectrum of hydrogen with a spectroscope.

The above series of four lines in the visible spectrum of hydrogen was named as the Balmer

Series. By carefully studying the wavelengths of the observed lines, Balmer was able empirically to

give an equation which related the wavelengths (λ) of the observed lines. The Balmer Equation is

1/λ=R( 1/2^2-1/n^2)

where R is a constant called the Rydberg Constant which has the value 109, 677 cm– 1 and n = 3, 4,

5, 6 etc. That is, if we substitute the values of 3, 4, 5 and 6 for n, we get, respectively, the wavelength

of the four lines of the hydrogen spectrum.

Blue-green Blue Violet

6563 4861 434

Balmer series in the Hydrogen spectrum. 

In addition to Balmer Series, four other spectral series were discovered in the infrared and

ultraviolet regions of the hydrogen spectrum. These bear the names of the discoverers. Thus in all

we have Five Spectral Series in the atomic spectrum of hydrogen :

Name                                  Region where located                        

(1) Lyman Series Ultraviolet ( 1)     UV

(2) Balmer Series Visible       (2)  visible

(3) Paschen Series Infrared  (3) Infrared

(4) Brackett Series Infrared   (4) infrared

(5) Pfund Series                     (5)infrared

    Balmer equation had no theoretical basis at all. Nobody had any idea how it worked so

accurately in finding the wavelengths of the spectral lines of hydrogen atom. However, in 1913 Bohr

put forward his theory which immediately explained the observed hydrogen atom spectrum. Before

we can understand Bohr theory of the atomic structure, it is necessary to acquaint ourselves with the

quantum theory of energy

CONTINUOUS SPECTRUM:

 White light is radiant energy coming from the sun or from incandescent lamps. It is composed of

light waves in the range 4000-8000 Å. Each wave has a characteristic colour. When a beam of white

light is passed through a prism, different wavelengths are refracted (or bent) through different

angles. When received on a screen, these form a continuous series of colour bands : violet, indigo,

blue, green, yellow, orange and red (VIBGYOR). This series of bands that form a continuous

rainbow of colours, is called a Continuous SpectrumWhite light is radiant energy coming from the sun or from incandescent lamps. It is composed of

light waves in the range 4000-8000 Å. Each wave has a characteristic colour. When a beam of white

light is passed through a prism, different wavelengths are refracted (or bent) through different

angles. When received on a screen, these form a continuous series of colour bands : violet, indigo,

blue, green, yellow, orange and red (VIBGYOR). This series of bands that form a continuous

rainbow of colours, is called a Continuous Spectrum

   The violet component of the spectrum has shorter wavelengths (4000 – 4250 Å) and higher

frequencies. The red component has longer wavelengths (6500 – 7500 Å) and lower frequencies.

The invisible region beyond the violet is called ultraviolet region and the one below the red is

called infrared region

Significance of the Henderson-Hasselbalch equation

Significance of the Henderson-Hasselbalch equation

With its help :

(1) The pH of a buffer solution can be calculated from the initial concentrations of the weak acid

and the salt provided Ka is given.

However, the Henderson-Hasselbalch equation for a basic buffer will give pOH and its pH can be

calculated as (14 – pOH).

(2) The dissociation constant of a weak acid (or weak base) can be determined by measuring the

pH of a buffer solution containing equimolar concentrations of the acid (or base) and the salt.

[salt] pH = p + log [acid]

Ka

Since

[salt] [salt] = [acid], log log1 0 [acid] = =

∴ pKa = pH

The measured pH, therefore, gives the value of pKa of the weak acid.

Likewise we can find the pKb of a weak base by determining the pH of equimolar basic buffer.

(3) A buffer solution of desired pH can be prepared by adjusting the concentrations of the salt

and the acid added for the buffer.

It is noteworthy that buffer solution are most effective when the concentrations of the weak acid

(or weak base) and the salt are about equal. This means that pH is close to the value of pKa of the acid

(or pKb of the base).

Fusion as a source of energy in 21st century

 FUSION AS A SOURCE OF ENERGY IN 21st CENTURY

Almost likely that the world’s energy source in the twenty-first century will be a fusion reactor.

As indicated by the trends of research, it will be based on the reactions as:

1^1H + 2^ 1H  + ⎯⎯→ 2^3He +1^On+ energy 

2 ^1H +3^1H  ⎯⎯→ 4^2He+ 1^On +energy

A fusion reactor thus developed will be any time superior to a fission reactor for generating

electricity.

1. The fusion fuel, deuterium ( 2

1 H ), can be obtained in abundance from heavy water present

in sea water. The supplies of U-235 needed for a fission reactor are limited.

2. A fusion reaction produces considerably greater energy per gram of fuel than a fission

reaction.

3. The products of fusion ( 3

2He , 4

2He ) are not radioactive. Thus, there will be no problem of

waste disposal.

So far, it has not been possible to set up a fusion reactor. The chief difficulty is that the reactant

nuclei must be heated to very high temperatures. A mixture of deuterium and tritium nuclei, for

example, requires 30 million °C before they can fuse. So far no substance is known which can make a

container that could with stand such high temperatures. However, scientists are making efforts to

effect fusion at a lower temperature with the help of las

Definition of Artificial Radioactivity

 ARTIFICIAL RADIOACTIVITY

Many stable nuclei when bombarded with high speed particles produce unstable nuclei that are

radioactive. The radioactivity produced in this manner by artificial means is known as artificial

radioactivity or induced radioactivity.  

Wave Nature Of Electron

 THE WAVE NATURE OF ELECTRON

de Broglie’s revolutionary suggestion that moving electrons had waves of definite wavelength

associated with them, was put to the acid test by Davison and Germer (1927). They demonstrated the

physical reality of the wave nature of electrons by showing that a beam of electrons could also be

diffracted by crystals just like light or X-rays. They observed that the diffraction patterns thus

obtained were just similar to those in case of X-rays. It was possible that electrons by their passage

through crystals may produce secondary X-rays, which would show diffraction effects on the

screen. Thomson ruled out this possibility, showing that the electron beam as it emerged from the

crystals, underwent deflection in the electric field towards the positively charged plate

de BROGLIE’S EQUATION:

 de BROGLIE’S EQUATION

de Broglie had arrived at his hypothesis with the help of Planck’s Quantum Theory and Einstein’s

Theory of Relativity. He derived a relationship between the magnitude of the wavelength associated

with the mass ‘m’ of a moving body and its velocity. According to Planck, the photon energy ‘E’ is

given by the equation

E = hν ...(i)

where h is Planck’s constant and v the frequency of radiation. By applying Einstein’s mass-energy

relationship, the energy associated with photon of mass ‘m’ is given as

E = mc2 ...(ii)

where c is the velocity of radiation

Comparing equations (i) and (ii)

mc2 = hν = c h

λ

⎛ ⎞ c ⎜ ⎟ ν = ⎝ ⎠ λ

∵

or mc = h

λ ...(iii)

or mass × velocity = wavelength

h

or momentum (p) = wavelength

h

or momentum ∝ 1

wavelength

The equation (iii) is called de Broglie’s equation and may be put in words as : The momentum

of a particle in motion is inversely proportional to wavelength, Planck’s constant ‘h’ being the

constant of proportionality.

The wavelength of waves associated with a moving material particle (matter waves) is called de

Broglie’s wavelength. The de Broglie’s equation is true for all particles, but it is only with very small

particles, such as electrons, that the wave-like aspect is of any significance. Large particles in motion

though possess wavelength, but it is not measurable or observable. Let us, for instance consider de

Broglie’s wavelengths associated with two bodies and compare their values.

(a) For a large mass:

Let us consider a stone of mass 100 g moving with a velocity of 1000 cm/sec. The de Broglie’s

wavelength λ will be given as follows :

λ =

27 6.6256 10

100 1000

− ×

× momentum

⎛ ⎞ h ⎜ ⎟ λ = ⎝ ⎠

= 6.6256 × 10– 32 cm

This is too small to be measurable by any instrument and hence no significance.

(b) For a small mass:

Let us now consider an electron in a hydrogen atom. It has a mass = 9.1091 × 10– 28 g and moves

with a velocity 2.188 × 10– 8 cm/sec. The de Broglie’s wavelength λ is given as

λ =

27

28 8

6.6256 10

9.1091 10 2.188 10

−

− −

×

×× ×

= 3.32 × 10– 8 cm

This value is quite comparable to the wavelength of X-rays and hence detectable.

It is, therefore, reasonable to expect from the above discussion that everything in nature possesses

both the properties of particles (or discrete units) and also the properties of waves (or continuity).

The properties of large objects are best described by considering the particulate aspect while

properties of waves are utilized in describing the essential characteristics of extremely small objects

beyond the realm of our perception, such as electrons.

QUANTUM THEORY OF RADIATION:

 

The wave theory of transmission of radiant energy appeared to imply that energy was emitted

(or absorbed) in continuous waves. In 1900 Max Planck studied the spectral lines obtained

from hot-body radiations at different temperatures. According to him, light radiation was produced

discontinuously by the molecules of the hot body, each of which was vibrating with a specific frequency

which increased with temperature. Thus Planck proposed a new theory that a hot body radiates

energy not in continuous waves but in small units of waves. The ‘unit wave’ or ‘pulse of energy’ is

called Quantum (plural, quanta). In 1905 Albert Einstein showed that light radiations emitted by

‘excited’ atoms or molecules were also transmitted as particles or quanta of energy. These light

quanta are called photons.

The general Quantum Theory of Electromagnetic Radiation in its present form may be stated

as :

(1) When atoms or molecules absorb or emit radiant energy, they do so in separate ‘units

of waves’ called quanta or photons. Thus light radiations obtained from energised or

‘excited atoms’ consist of a stream of photons and not continuous waves.

(2) The energy, E, of a quantum or photon is given by the relation

E = hν ...(1)

where ν is the frequency of the emitted radiation, and h the Planck’s Constant. The value

of h = 6.62 × 10– 27 erg sec. or 6.62 × 10– 34 J sec.

We know that c, the velocity of radiation, is given by the equation

c = λν ...(2)

Substituting the value of ν from (2) in (1), we can write

E = hc/λ

Thus the magnitude of a quantum or photon of energy is directly proportional to the

frequency of the radiant energy, or is inversely proportional to its wavelength, λλλ.

(3) An atom or molecule can emit (or absorb) either one quantum of energy (hννν) or any

whole number multiple of this unit.

Thus radiant energy can be emitted as hν, 2hν, 3hν, and so on, but never as 1.5 hν, 3.27 hν,

5.9 hν, or any other fractional value of hν i.e. nhν

Quantum theory provided admirably a basis for explaining the photoelectric effect, atomic

spectra and also helped in understanding the modern concepts of atomic and molecular structure

QUANTUM THEORY AND BOHR ATOM: Rutherford model laid the foundation of the model picture of the atom. However it did not tell anything as to the position of the electrons and how they were arranged around the nucleus. Rutherford recognised that electrons were orbiting around the nucleus. But according to the classical laws of Physics an electron moving in a field of force like that of nucleus, would give off radiations and gradually collapse into the nucleus. Thus Rutherford model failed to explain why electrons did not do so. Neils Bohr, a brilliant Danish Physicist, pointed out that the old laws of physics just did not work in the submicroscopic world of the atom. He closely studied the behaviour of electrons, radiations and atomic spectra. In 1913 Bohr proposed a new model of the atom based on the modern Quantum theory of energy. With his theoretical model he was able to explain as to why an orbiting electron did not collapse into the nucleus and how the atomic spectra were caused by the radiations emitted when electrons moved from one orbit to the other. Therefore to understand the Bohr theory of the atomic structure, it is first necessary to acquaint ourselves with the nature of electromagnetic radiations and the atomic spectra as also the Quantum theory of energy