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CONTENTS 1.) INTRODUCTION 2.) HISTORY 3.) PROPERTIES 4.) SPECTRA 5.) ENERGY LEVELS OF HELIUM 6.) ORTHO HELIUM & PARA HELIUM 7.) GROUND STATE ENERGY OF HELIUM ATOM BY VARIATIONAL METHOD 8.) USES & APPLICATION

Helium Front

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Page 1: Helium Front

CONTENTS

1.) INTRODUCTION2.) HISTORY3.) PROPERTIES4.) SPECTRA5.) ENERGY LEVELS OF HELIUM 6.) ORTHO HELIUM & PARA HELIUM7.) GROUND STATE ENERGY OF HELIUM ATOM BY VARIATIONAL METHOD8.) USES & APPLICATION

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INTRODUCTION

HELIUM ATOM- Atom of chemical element Helium composed of 2 electrons bound by em force to nucleus containing 2 protons along with either one or two neutrons depending on isotope Belongs to 18th group & 1st period in periodic table Belongs to s- group At 20 degree centigrade: present in gas state Electronic configuration: 1s2

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HISTORY

1868 – first evidence was observed as a bright yellow line with a wavelength of 587.49 nm in the spectrum of sun. The line was detected by French astronomer Jules Janseen during a total solar eclipse in India

1882- Italian physicist Luigi Palmieri detected helium on earth for the very first time

1895– Sir William Ramsay isolated Helium on earth by treating the mineral cleveite (variety of uranite with atleast 10% rare earth elements) with mineral acids independently isolated from cleveite by Per Theodor Cleve & Abraham Langlet in Sweden

William Ramsay (1852-1916 )

Per Theodor Cleve (1840-

1905 )

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PROPERTIES OF HELIUM

Colorless, odourless, gaseous non metallic elementAtomic number: 2Atomic mass : 4.00260 g. molMelting point : - 272.2 0CBoiling point : - 268.9 0CLow solubilityLess reactive element & doesn’t form chemical compound2nd most common element (after hydrogen) in universe, making up around 24% of its massHelium is a part of a group of chemical elements called noble gases, the 5 other that occur naturally are- neon, argon, krypton, xenon & radon Is the only gas which is capable of reaching temp. lower than 15K (-4340F)

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SPECTRA

1.) CONTINUOUS SPECTRUM: It is a continuous bright region with all the wavelengths of the selected region present.

2.) EMISSION SPECTRUM: Spectrum of frequencies of em radiation emitted due to an atom or molecule making transition from high energy state to a lower energy state.

3.) ABSORPTION SPECTRUM: The characteristic pattern of dark lines or band that occurs when em radiation is passed through an absorbing medium into a spectroscope.

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SPECTRA OF HELIUM ATOM

This is the pattern of wavelengths emitted by the element helium.

This is the pattern of wavelengths of helium that is found in the light from distant stars and galaxies. It's helium because the pattern is the same but notice that all the wavelengths are shifted towards the red end of the spectrum.

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the greater the amount of shift, the faster the star is moving!

Helium

Helium slightly red shifted. Moving away.

Helium more red shifted. Moving away even faster!

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HELIUM ENERGY LEVELS

Ground state consists of 2 identical 1s electrons . The energy required to remove one of them is the highest ionization energy of any atom in periodic table (24.6 ev).

energy required to remove 2nd electron is 54.4ev

the description of any electron in a multi- electron atom must find a way to characterize the effect of other electrons on the energy

An electron in upper state can have spin - antiparallel to the ground state electron ( s=0, singlet

state, parahelium) Parallel to the ground state electron (s=1, triplet state,

orthohelium)

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HELIUM ENERGY LEVELS

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Facts from this diagram-

For each singlet state there is corresponding triplet energy state, but no triplet state corresponding to the ground singlet state of He- atom triplet state lies little deeper than the corresponding singlet states energy difference between the ground state & lowest excited state is relatively large triplet state do not combine with the singlet state orthohelium atom can lose excitation energy in a collision & become an atom of parahelium, whereas a parahelium atom can gain excitation energy in a collision & become an atom of orthohelium. example: ordinary helium

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ORTHOHELIUM & PARAHELIUM ENERGY LEVELS

It is observed that orthohelium state are lower in energy than parahelium states.Because— parallel spin makes the spin part of the wavefunction symmetricTotal wavefunction for the electrons must be anti-symmetric , since they are fermions & must obey Pauli’s Exclusion Principle wavefunction can be written as the product of space & spin parts of the wavefunctionAntisymmetric space wave function for 2 electrons implies a larger average distance between them then a symmetric function of same type

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GROUND- STATE ENERGY OF HELIUM ATOM BY VARIATIONAL METHOD

VARIATIONAL METHOD

It is the main appropriate method used in quantum mechanicsAs compared to perturbation theory, the variation method can be more robust in situations where it’s hard to determine a good unperturbed HamiltonianIn cases where there is a good unperturbed Hamiltonian , perturbation theory can be more efficient than the variational method

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GROUND STATE ENERGYThe Helium atom has 2 electrons with coordinates r1 and r2 as well as a single nucleus with coordinate R. The nucleus carries a Z = +2e charge, the quantum- mechanical Hamiltonian operator is,

Where is the positive P.E. due to the coulomb (repulsive) interaction between the electrons. On neglecting the magnetic spin- orbit and spin- spin interactions between the electrons as these are very small compared to the coulomb interaction. Also neglecting the nuclear motion . The wave equation for the He-like atom can be written as,

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Unperturbed energy in the ground state is, E◦ = - 2 Z2 EH

= - 8 EH because Z= 2 for He = - 8 (13.6 ev) = - 108.8 ev

But the experimental value of the ground state energy of He- atom is -78.98 ev, which is very much different from the calculated value for the unperturbed ground state.

the unperturbed system provides a poor description of the energy levels

the coulomb interaction between the 2 electrons plays an important role in the behaviour of He- atom

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Considering the coulomb repulsion as a perturbation.Due to the first order perturbation correction , the total energy of the ground state of He- like atom is, E = E◦ + E’ = - 108.8 ev + 34.0 ev = - 74.8 ev

which is nearly equal to the experimental value, with an error of about 5%.

The first order perturbation theory cannot be expected to give very accurate results. For a greater accuracy, the variation method should be applied.

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USES & APPLICATIONS

Because helium is lighter than air it is used to fill air ships, blimps and balloons, as it doesn’t burn or react with other chemicals

Large hadron collider uses liquid helium to maintain an extremely low temperature

It is often used in space programs, displacing fuel in storage tanks and having other rocket fuel applications

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Contd...

It is also used to detect leaks, such as in car A.C. systems, & because it diffuses quickly it is used to inflate car airbags after impact

Mixture of 80% helium & 20% oxygen is used as an artificial atmosphere for deep sea divers & others working under pressurised conditions

Helium- neon gas lasers are used to scan barcodes in supermarket checkouts

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REFERENCES

1.) Elements of spectroscopy by Gupta, Kumar & Sharma (Pragati Prakashan Publication , 24th edition)

2.) Atomic and molecular spectra: Laser by Rajkumar (Kedar Nath Ram Nath Publication, 15th edition reprint, 2015)

3.) Helium: bibliography of technical and scientific literature from its discovery (1868) to January 1, 1947 by Wheeler , H.P. Jr. ; Swenarton L.B.

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THANKYOU