Non-relativistic model of helium atom In the helium atom the two electrons in the 1s orbit are stable with positive binding energy. They have both kinetic energy due to its motion in the circular orbit and potential energy due its position in the electrostatic field within the atom. The kinetic energy of an electron is (1/2) mv2 and for both the electrons which are identical in the system K.E is mv2. The electron is stable in the orbit by balancing out the resultant electrostatic force with the centrifugal force due to circular motion. Let us suppose that the two electrons are in the 1s orbit itself having radius r1.The centripetal force acting on an orbital electron due to nuclear attraction is 2e2 /Kr12 . The other electron in the same orbit is repelled by the electron already existing there and both of them are positioned at opposite end of a diameter of the orbit. If electron-electron interaction is not allowed in the same orbit, the relative position of these two electrons may vary from time to time. Then different helium atom with different placement of electrons in the orbit may exist .Since all helium atoms have identical spectral feature the electrons in an orbits take fixed relative position that is invariant with respect to time. The electrostatic force of repulsion between the two electrons which are diametrically opposite is e^2/4Kr1^2. The resultant force is balanced by centrifugal force i.e., 2e^2/Kr1^2 - e^2/ 4Kr1^2 = (7/4)e^2/Kr1^2 = mv1^2/r1 . The radius of the orbital electron in helium atom can be determined from the condition on its quantized angular momentum. It gives rn = n^2(4/7) ao. = 0.5714 n^2 ao. If we ignore the electron-electron interaction rn = ao/2 .The radius of the 1s orbit in He+ ion is increased by 0.0714 ao due to mutual electron-electron interaction in helium atom. Total kinetic energy of the electrons in the helium atom = mv1^2 = (7/4) e^2/Kr1 kinetic energy per electron = (1/2) mv1^2 = (7/8)e^2/Kr1 = (7/4) e^2/2Kr1 Potential energy of electron 1 = - 2 e^2/Kr1 Potential energy of electron 2 in the presence of electron 1 = - 2 e2 /Kr1 + e2 /2Kr1 Total potential energy of the electrons in the helium atom = - (7/2) e2/Kr1 Sum of K.E and P.E is - (7/4)e^2/Kr1 = - (49/8)[e^2/2Kao]= -6.125 x 13.595 = -83.269 eV which gives enough binding energy to the system. It gives the first ionization energy 83.269 - 54.368 = 28.901 eV. The experimental value of first ionization energy of helium is 24.481 eV which is 4.41 eV smaller than the theoretically predicted value.

Application of Bohr's Theory to He+ The line spectrum of the He+ ion will resemble that of the hydrogen atom (H) because both are one-electron system. They behave similarly at the quantum level despite different nuclear charges. Due to strong attractive force, the orbital electron in helium comes more closure to the nucleus and has more binding energy. Although the energy levels and wavelengths for He+ will be different (shifted to shorter wavelengths) due to the stronger nuclear pull, the overall pattern of spectral lines from electron transitions remains analogous. The electrostatic force on the electron equals with centrifugal force 2e2/K rn2 = m vn2/rn, m vn^2 rn = e^2/2πεo = constant ...... (2.1) Bohr's first condition-1 concerned with angular momentum requires mvnrn = nh/2π . Solving for rn, one can show that rn = n2 h2 εo / 2 mπ e2 = n2ao/2 .i.e., the radius of the innermost orbit in the helium ion is half the corresponding value of hydrogen atom. It can be shown that the radius of the innermost orbit in hydrogen like ions with atomic number Z is ao/Z. The orbital electron has both kinetic energy due to its orbital motion and potential energy by virtue of its position in the electrostatic field of the nucleus. Kinetic energy of the electron in the innermost orbit = (1/2) m v12 = e2 /Kr1 and its potential energy is -2e2 / Kr1 which together gives its total energy T.E = - e^2/ Kr1 .Substituting the value for r1 = h^2 K/8π^2 m e^2 , E1→∞ = [2e^2 /Kao ]= 4 (13.595) eV. In the case of hydrogen, it is E1→∞ = e^2/2Kao = 13.595 eV, which is 4 times lower than that of the helium ion. When the electron is in the innermost orbit of helium ion He+, its energy is 4 x 13.595 = 54.38 eV , The second ionization energy of helium atom is 54.40 eV which is in close agreement with the computed value. Its spectral feature can be studied by determining the electron transition energy and the corresponding wavelength of radiation emitted. ΔE = E excited /initial - E ground / final =4[13.595][(1/n1^2 - 1/n2^2)] , n2 > n1 The frequency of the emitted radiation ν = ΔE/h = 4[13.595/h][(1/n1^2 - 1/n2^2)] The wavelength of the emitted radiation λ = C/ν = hc/4(1/n1^2 - 1/n2^2)13.595 The Lyman series of helium ion corresponds to electronic transition from n ≥ 2 to n =1. The wavelength of emitted radiation λ = [6.626 x 10^-34 x 2.998 x 10^8]/4[13.595 x 1.602 x 10^-19][1/(1/n1^2 - 1/n2^2) = 0.2280 x 10-7 x ][1/(1/n12 - 1/n22) n2→n1; 0.2280 x 10^-7 x 4/3 = 30.40 nm n3→n1; 0.2280 x 10^-7 x 9/8 = 25.65 nm n4→ n1; 0.2280 x 10^-7 x 16/15 = 24.32 nm The limit of the series n∞→ n1: 22.80 nm The Balmer series of helium ion He+ contain the following wavelengths n3→ n2 ; 0.2280 x 10^-7 x 36/5 = 164.16 nm n4→ n2; 0.2280 x 10^-7 x 16/3 = 121.60 nm n5→ n2; 0.2280 x 10^-7 x 100/21 = 108.57 nm The limit of the series n∞→ n2: 91.20 nm The Paschen series of helium ion He+ contain the following spectral lines n4→ n3 ; 0.2280 x 10^-7 x 144/7 = 469.02 nm n5→ n3; 0.2280 x 10^-7 x 225/16 = 320.62 nm n6→ n3; 0.2280 x 10^-7 x 12 = 273.60 nm The limit of the series n∞→ n3: 205.20 nm The wavelengths of the He+ ion spectrum are specific to the electron transitions between energy levels and are calculated by using the Rydberg formula, for example the 2p to 1s transition gives a wavelength around 30.3 nm. In the Balmer series, the second line (n=4 to n=2) has a wavelength of approximately 121.6 nm. The Paschen series of He+ consists of infrared wavelengths . The hydrogen, helium ion and helium atom all together contribute the ultraviolet (UV) spectrum of the sun usually it ranges from approximately 100 to 400 (nm) in wavelength. This spectrum is divided into three main bands: UVA (315–400 nm), UVB (280–315 nm), and UVC (100–280 nm). Most of the UVA and UVB radiation reaches the Earth's surface, while the ozone layer absorbs almost all UVC radiation. Relativistic Bohr Model of He+ Both the non-relativistic and relativistic approaches to helium ion Bohr's model gives same result. Applying the law of conservation of energy 2e^2/Krn = (1/2)mn vn^2 + dmnc^2 = (1/2) mo vn^2 + dmn c^2/(1-vn^2/c^2)^1/2) e^2/Krn = dmn c^2 = (mn - mo) c^2 ≃ (1/2) mo vn^2 , where rn = (n^2/2)ao [1-vn^2/c^2]^1/2 .By solving the relations for the nuclear attractive force and the orbital angular momentum vn = e2/nhεo .Substituting this value in dm c^2 dmnc^2 = mo e^4/2n^2h^2 εo^2 = (1/n^2)4 [e^2/2Kao] = [54.38/n2] eV = (1/n^2)[4e^2/2Kao]/[1 - vn^2/c^2]^1/2 Where vn = e^2/nhεo. When the electron is in the innermost orbit of helium ion, dm1c^2 will represent the atomic binding energy . dm1c^2 = [4 x 13.595][1 - e^4/h^2εo^2c^2]^1/2 = 54.38 x 0.99989 = 54.37 eV The spectral lines are the electromagnetic radiation due to the difference of binding energies of the final and initial positions of the electron in the system. [(dm)f - (dm)i]c^2 = (1/2)mo[vf^2 - vi^2] = (1/2) mo[e^4/h^2εo^2][1/nf^2 - 1/ni^2] = 4[e^2/2Kao][1/nf^2 - 1/ni^2] For a known spectral line in the spectrum of He- ion, the possible electronic transition between the energy levels can be predicted. For example λ = 320 nm, Using the above relation one can identify which transitions will give this wavelength . ΔE = hc/λ = 54.38[1/nf^2 - 1/ni^2] (ni^2 - nf^2)/ni^2 x nf^2 = 0.07125 For the positive values of both ni and nf , the best amicable value of nf =3. ni^2 - 9 = 0.07125 x 9xni^2 = 0.64125 ni^2 or 0.35875 ni^2 = 9 or ni = 5.0087 .It becomes 5 after adjusted to nearest whole number.If there are two or more possibilities for a any particular line, that would be more intense.

கடவுள் நம் முன்னோர்களால் கற்பிக்கப்பட்ட ஒரு கருத்து . மனிதர்கள் எல்லோரும் அவர்களுடைய மனதை தாங்களாகவே சுத்தப்படுத்திக் கொள்ள அந்தக் கருத்து நிலைநிறுத்தப்பட்டது . அதை அறிவுரை என்றோ , ஆன்மிகம் என்றோ, இல்லை பயமுறுத்தும் கட்டளை என்றோ எப்படிவேண்டுமாலும் எடுத்துக்கொள்ளலாம் .நாம் எப்படி எடுத்துக்கொள்கின்றோம் என்பதை ப் பொறுத்து கடவுளின் தோற்றம் நமக்குள் வேறுபடுகின்றது

கடவுள் கடவுளாகவே இருக்கும் வரை கடவுளால் மனிதர்களுக்கு எந்த வொரு பயனுமில்லை. அங்கே கடவுள் ஒரு வியாபாரப் பொருளாகிவிடுகின்றார் . கடவுள் மனிதனாக அவதரிக்கவேண்டும் அல்லது மனிதன் கடவுளாக உயரவேண்டும் . அப்பொழுதுதான் மனிதகுலம் கடவுளால் மேன்மையடையும்

ஏமாற்றுபவர்கள் ஏமாந்தவர்களை ஏமாற்றினால் நீங்கள் யாரை குறைகூறுவீர்கள் ? ஏமாற்றுபவர்களையா அல்லது ஏமாந்து போவோர்களையா ? என்னைக் கேட்டால் நான் ஏமாற்றுபவர்களையே தண்டிக்க வேண்டும் என்று கூறுவேன் . கோழியா இல்லை முட்டையா எது முதலில் வந்தது என்பதைப்போல முதலில் வந்தது ஏமாற்றுபவர்களா அல்லது ஏமாந்துபோவோர்களா ? ஏமாற்றுபவர்கள் இல்லாவிட்டால் ஏமாந்துபோவோர்கள் இருக்க மாட்டார்கள் .ஏமாந்தவர்கள் என்ற இனம் இயற்கையாக வந்ததில்லை .அது ஏமாற்றுபவர்களினால் மட்டுமே உருவானது . ஏமாற்றுவது என்பது சார்பில்லாத தன்னிச்சையான செயல் . ஏமாறுவது என்பது சார்புறு செயல்.எனவே முதலில் கட்டுபடுத்த வேண்டியது ஏமாற்றுபவர்களையே ஏமாற்றுதல் ,ஏமாறுதல் என்ற வினைச் செயல்களில் ஏமாற்றுதல் மட்டுமே தன்வினைச் செயல் , ஏமாறுதல் என்பது எம்மாற்றப்படுவதை தடுத்துக்கொள்ள செய்யவேண்டிய எதிர் வினைச் செயலின் செயலின்மை .ஒருவன் நேர்மையாக சமுதாயத்தோடு இணக்கமாக வாழ இந்த இரு வினைகளுமே தேவையில்லை. நேர்மைத்தவறி வாழ நினைப்பவர்கள் ஏமாற்றுவதை த் தொழிலாகக் கொள்கின்றார்கள் . ஏமாற்றுவது வந்ததால்தான் ஏமாறுவது வந்தது. ஏமாற்றுவது இல்லையென்றால் ஏமாறுவதும் இல்லை .ஏமாற்றுவது என்பது இயற்கையின் பார்வையில் மனித இயல்பு இல்லை . அது தீயவர்களின் தீய பண்பு. இது எப்போதும் மறைவொழுக்க நடவடிக்கைகளாகவே இருக்கும் ஏமாற்றுபவர்கள் இயற்கையின் வரம்பிற்கு அப்பாற்பட்டு இயல்புநிலைக்கு மீறிய இயல்புகளை வளர்த்துக்கொள்ள வேண்டியிருக்கு . ஆனால் ஏமாற்றப்படுவோம் என்பதை அறியாமல் அதை தடுத்துக் கொள்ள முன்னெச்சரிக்கை நடவடிக்கைகளை கற்றுக்கொள்ளாமல் போவதால் ஏமாந்துபோவோர்கள் ஏமாந்து போகின்றார்கள்

Human Psycology A person by appearence is single but his mind is always double - one is open and other is hidden. Every human being possesses two distinct types of minds. Generally, these two minds do not align with each other. The reason for this is that every individual has created and cultivated one mind for themselves and another for society. An open social mindedness is develpned as a way to demonstrate concern for the community's well-being—ensuring one is not ostracized while living within it. Usually the open mindedness is exposed when the person is in a group or among public with an aim that the other will think high about him when this persona is genuine, the individual is largely a good person, whereas when it is feigned, they tend to be somewhat malevolent. In contrast, the mind that contemplates self-interest while in solitude differs from this open social persona, effectively causing the individual to don a mask.The nature of these two minds of a person can be seen by throwing 500 rupee note in the street in which he passes by, if he is alone he may take the money and keep in his packet ,it is done as said by his own and hidden mind. If he is walking along with few unknown public, he will pretend by searching the money loser ultimately he will put it in a hundi in temple. These two different minds determines the real character of a person. A person cannot be 100 % good or 100 % bad The percentage of mixing of these two minds measures how good or bad a person is.

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