Current Math Problems - Essay Example

?1a) i. The lowest level in the hydrogen atom is level two n=2 which is involved in all transitions for the absorption lines in the visible region ofthe spectrum. ii. -1.0826 eV is required to ionize hydrogen from this level and te formula is given as E = -R/n^2, where R = Rydberg's (energy) constant = 13.598 eV*, and n = shell number that the electron is in. iii. -10.2eV visible 1b) i) proton and neutron are the subatomic particle present in Helium ion,2proton and 2 neutron are there,and the energy level is also shifted because in helium 2 proton and 2 neutron are there while in hydrogen 1 proton and no neutron are there that’s why energy levels are shifted. ii) -1.89 lie in IR region. 1c)Because its closer to the nucleus and having some effect on the other electron present in the higher shell Q2 a) Power output of sun = 3.8 *1026W Radius = 1.4 * 108 Power density = ? V= 4/3 ?r3 V= 4/3 ? (1.4*108)3 =1.15*1025 Power density: Power/volume = 3.8*1026/1.15*1025 1ev= 1.6*10-19J Total energy released for He nucleus is 26.7 Mev 26.7*106*1.6*10-19 4.27*10-12 energy is released for 1 he atom =>3.8*1026 J produce 3.8*1026/4.27*10-12 *1/(4*?*(1.4*108)3/3) Helium atoms per second per cubic meter (here assume time =1sec therefore energy =3.8 *1026W *1sec 7.74*1012 Helium atoms per second per cubic meter 2b) In He both the nucleons are there means protons and neutron,2 protons and 1 neutron is there. In first equation there are less number of nucleons involve so there nuclear force will be less and thus it will be more reactive there fore they are less stable while on the other hand when the nucleons are more in number as it is in step 2 therefore there will be strong nuclear force, will be less reactive and more stable. 2c) When the fusion reaction occurs so at that time two atoms combine and produce larger atom and release high energy in the form of binding energy of nucleons. As this process continues till the formation of iron Fe 56,so at that time binding energy of electron is minimum that is most negative and now if the more heavier atom is required to be formed so more energy will release Q3 a i) Data: Redshift = z = 0.13 Speed of light =c= 3 * 108 ms-1 Hubble constant = H0 = 70 kms-1Mpc-1 Distance to the galaxy = r=? Formula: 1. H0 = v / r Here v = apparent speed of galaxy 2. v = z * c Solution: v = z * c =0.13 * 3 * 108 v = 3.9 * 107 ms-1 v = 3.9*107*10-3kms-1 v = 3.9*104 kms-1 H0 = v / r r= v / H0 r = 3.9*104 /70 r = 5.57*102 Mpc Q3 a ii) Data Red shift =z = 0.13 ?0=589nm ?1=? Formula ??=?1-?0 z=??/?0 Solution z= ??/?0 0.13= ??/589 ??=76.57nm ?1-?0 =76.57 ?1 =76.57+589 ?1=665.57nm ?1=6.65*102 nm Q3 b i) As the wavelength of hypothetical object is different as compare to the wavelength of the objects which are already present in the cluster and this wavelength is very large which causes this hypothetical object to move out of the galaxy that’s why that this object is not part of this cluster, and is actually more distant. Q3 b ii) The answer is not in the book. Or no relative material is in the book kindly search yourself Q#4 General relativity and quantum gravity depart from Newton’s theory. The gravitational force of attraction is described by Newton’s law of gravity. Einstein’s theory of general relativity describes the interaction between space and the matter within it. When the masses become very large, this theory provides a more accurate description of gravity than does Newton’s law. General relativity also predicts the existence of gravitational radiation, which is emitted by massive objects that undergo an acceleration. There is good evidence that such radiation is being generated by binary pulsars. A convincing theory of quantum gravity has yet to be formulated, but it will involve quanta referred to as gravitons which interact with everything. Einstein’s theory of general relativity reproduced all the old results of Newton, but without even using the idea of weight. The core of general relativity is the interaction between ‘space’ and the ‘matter’ within it. One of its basic conclusions is that objects that possess mass change the geometry of space,causing it to be ‘curved’. The curvature of space then controls the movement of material objects within it. It has been said that ‘matter tells space how to curve’ and ‘space tells matter how to move’. Gravitational effects arise as a result of the curvature of space. Taking the Solar System as an example, the Sun causes space to curve in its vicinity. The orbits of the Earth and the other planets are then a consequence of their movement through this curved space. Newton’s law of gravitation is able to predict what is actually observed in a wide variety of situations. But it is only an approximation to the real world and no longer provides satisfactory answers when the masses involved become very large. Similarly, whilst Einstein’s general relativity can cope with such situations accurately, that too fails when physicists try to unite it with the ideas of quantum physics. So general relativity too may be only an approximation to some deeper, underlying truth. Nearly a hundred years after Einstein’s great work we still do not have a proper relativistic quantum theory of gravity, usually referred to simply as a theory of quantum gravity . There are two reasons why we still have not got such a theory. First, there is practically no experimental data on the interplay of gravity and quantum physics, because gravity is so weak at the level of individual particles. The second problem is a conceptual one. that the quantum physics of atoms involves uncertain velocities and positions for the electrons. In a quantum theory of gravity, somehow the notions of space and time themselves would have to become uncertain. In non-gravitational quantum physics you cannot be sure exactly what you will measure, here and now, or there and then. In a quantum theory of gravity, you would be unsure of what here and now, or there and then, might mean! Despite these difficulties, it is believed that quanta of gravitational energy exist. They are known as gravitons and have zero electric charge and zero mass. It is predicted that gravitons interact with everything; not just material bodies with mass, but also photons and gluons, which have no mass, and even neutrinos, whose masses are as yet poorly known. Moreover, gravitons are predicted to interact with other gravitons too. That makes photons the unique quanta that do not interact significantly with themselves. Read More