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## At just 10[math]^{-12}[/math] seconds after the Big Bang the universe is believed to have been expanding at 10[math]^{29}[/math] times the rate it is now. Why is that?

At just 10[math]^{-12}[/math] seconds after the Big Bang the universe was believed to have been expanding at 10[math]^{29}[/math] times the rate it is now. Why is that?Corrections: If Guth’s “inflation” conjecture would hold true — and if using Guth’s original numbers — the extremely short-lived “inflation epoch” began at “Universe age” 10[math]^{-35}[/math] s, and ended 3[math]×[/math]10[math]^{-30}[/math] s “later” (at which “time” the infant Universe abruptly resumed its more leisurely expansion rate c (lightspeed), which it has retained ever since.[math]^1[/math] Using Guth’s original numbers, the rate at which the Universe was “expanding” during the inflation event was [math]\approx[/math] 5[math]×[/math]10[math]^{23}[/math]c. The question itself remains.Short answer: The hyperluminal expansion rate is in theory attributed to what took place during the hypothetical “Inflation Epoch” (invented by Alan H. Guth, first published in his seminal paper Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems (Phys. Rev. D, August 1980)).From Wikipedia article Inflationary Epoch:In physical cosmologythe inflationary epoch was the period in the evolution of the early universewhen, according to inflation theory,the universe underwent an extremely rapid exponential expansion.This rapid expansion increased the linear dimensions of the early universe by a factor of at least 10[math]^{26}[/math] (and possibly a much larger factor), and so increased its volume by a factor of at least 10[math]^{78}[/math]. Expansion by a factor of 10[math]^{26}[/math] is equivalent to expanding an object 1 nanometer (10[math]^{−9}[/math] m, about half the width of a moleculeof DNA)in length to one approximately 10.6 light years(about 62 trillion miles) long.It is a rather intriguing idea: an extremely short time “post bang,” the “Planck length scale”young Universe “fluffed up” from [math]\approx[/math] 10 000 000 times smaller than a proton, to the comparatively enormous size of a bowling ball![math]^2[/math]Here’s a “timeline,” in numbers: The size of the Universe, from the age of one Planck time (i.e., [math]\approx[/math] 10[math]^7[/math] times smaller than a proton), to one second (a 10 cm radius sphere, 10[math]^{26}[/math] times the non-inflated radius ). The “inflation epoch” is shaded pink, the “ages” one Planck time and one second are shaded blue (the 10[math]^{-12}[/math] s age is shaded green):The pink shaded “inflationary epoch” rows unlock the answer: these three rows represent the speed by which the virtual surface of the expanding Universe races away from the origin — [math]\approx[/math] 5[math]×[/math]10[math]^{23}[/math]c.In the following log-log graph of the Universe expansion from time T[math]_0[/math] to the present, the above table resides in the lower left-hand quadrant:Footnotes[math]^1[/math] This would yield a present Universe radius of [math]\approx[/math] 13.83 Gly (billion lightyears). However, “modern high-precision cosmology” states that during all that time, due to a mysterious (and so far both unknown and undetected “dark energy”), the “metric” of space itself has expanded (!), “stretching” the present Universe radius to no less than [math]\approx[/math] 46.5 Gly. Cut from Wikipedia article Observable Universe(bold added for emphasis):The observable universe is a spherical region of the Universe comprising all matterthat can be observed from Earth at the present time, because electromagnetic radiation from these objects has had time to reach Earth since the beginning of the cosmological expansion.[…] That is, the observable universe has a spherical volume (a ball)centered on the observer.[…]According to calculations, the current comoving distance— proper distance, which takes into account that the universe has expanded since the light was emitted — to particles from which the cosmic microwave background radiation(CMBR) was emitted, which represent the radius of the visible universe, is about 14.0 billion parsecs(about 45.7 billion light-years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light-years), about 2% larger. The radius of the observable universe is therefore estimated to be about 46.5 billion light-years[math]^2[/math] Yes, you read that right: The pre-inflation Universe size (in theory) is to a bowling ball what a bowling ball is to [math]\approx[/math] 10 lightyears!

## Can I score 50/70 in the 12th class boards of physics by starting today? What should I do to only focus on derivations and theory?

You have studied whole the year. you have taken half yearly and pre boards exams. There must be everything in your head. It is only that the information is scattered in your mind. You have to consolidate that. Give a direction to your learning. The modern physics part is easiest, takes less time, problems are limited and are mostly from NCERT. So start from there. I am sure you can do that. You will do that. Have faith in you.In case of any doubt, you can contact me through my message box or through comment section. I am available 24 x 7.Important things are given in bold.Day 1, Session 1 : Communication (4 hours)Definitions of transducer, signal, attenuation, modulation, demodulation and repeater (page 516, 517 NCERT), point to point/broadcast mode of communicationAll block diagrams (there are only five such diagrams) with one function of each block.Figure 15.4 (given below, notice that [math]\nu_1 >\nu_2>\nu_3[/math]), 15.6, 15.8 (only amplitude modulation), 15.9 (a must).Basic things about ground wave, sky wave and space wave such as frequency range, factors limiting range, names of the services. Learn the formulae for range [math](\sqrt{2Rh_T})[/math] and maximum distance [math](\sqrt{2Rh_T}+\sqrt {2Rh_R})[/math]. No derivation required.Paragraph 15.7 (15.71, 15.72 and 15.73). Derivation of equation 15.5.Exercises no. 15.1 to 15.7. leave 15.8.Try to memorise table 15.2.Frequency and phase modulation is out of syllabus. However learn why frequency modulation is preferred over amplitude modulation.Day 1, Session 2: Atom (4 hours)Impact parameter and distance of closest approach. spectral series Just formulae)Observations, conclusions and drawbacks of Geiger and marsden experiment (no experimental details).Bohr’s postulates. Derivation of radius, speed and energy of an electron revolving in [math]n^{th}[/math] Bohr’s orbit using Bohr’s second postulate [math](mv_n r_n =n\frac h{2\pi})[/math] and [math]\frac 1{4\pi\epsilon_0} \frac{e^2}{r^2}=\frac{mv^2}{r^2}[/math]. Believe me this is easy. Or atleast learn the followings -A question will certainly be there that can be solved with the help of above three equations.De Broglie’s explanation of Bohr’s second postulate.Figure 12.3, 12.4, 12.9, 12.10.Solved example 12.2. Exercises 12.3 to 12.9, 12.15, 12.17.Day 1,Session 3 : (1 hour)Revise block diagrams and definitions of communication chapter. Revise derivation of v_n, r_n and E_n of an electron in nth Bohr orbit.Day 2, Session 1: Nuclei (4 hours)Size of nucleus [math](r = r_0 A^{1/3}, r_0 = 1.2 Fm)[/math]. Showing that the density of nuclear matter is independent of the size of the nucleus[math]Density = \frac {mass of the nucleus}{ volume of the nucleus} = \frac {mA}{4/3 \pi r^3} = \frac {mA}{4/3\pi r^3_0 A} = \frac{3m}{4 \pi r^3_0}[/math] which is independent of A.Numericals on binding energy, binding energy per nucleon (will come later for theory) exercises 13.3, 13.4 ( note that this question is about binding energy per nucleon, a misprint in the NCERT), 13.5.Numericals on [math]\alpha, \beta and \gamma[/math] decay (will come later for theory). Solved examples 13.1, 13.6. Exercises 13.12, 13.13, 13.14, 13.29.Take 5 previous years’ question papers, solve all the 25 one-marker questions.Day 2, Session 2: Nuclei: (4 hours)Curve depicting ‘binding energy per nucleon as a function of mass number’ (figure 13.1) and the following questions on it. This part is very important.Important features of the graph:(i) The force is attractive and sufficiently strong to produce a binding energy per nucleon of a few MeV.(ii) Nuclear force is short ranged ( Explain points a b and c given below on the basis of this).(a) Consistency of binding energy per nucleon in the range 30 < A < 170.(b) Binding energy per nucleon decreases for A > 170.(c) Binding energy per nucleon is small and increases with increasing number of nucleons for A < 30.(iii) Energy can be obtained by fission of heavier nuclei. Explain how.(iv) Energy can be obtained by fusion of lighter nuclei. Explain how.Derivation of laws of radioactive decay [math](N = N_0 e^{-\lambda t}[/math], [math]R = R_0 e^{-\lambda t})[/math], Half life, mean life and relation between the two. Don’t spend much time on the derivations. If you can not do them, leave them, just learn the formulae.Exercise No. 13.6, 13.7, 13.9, 13.10, 13.16, 13.18, 13.19. Figure 13.2, 13.3 and 13.4. Leave paragraphs 13.7 (13.71 and 13.72)Day 2, session 3: (1.5 hours)Solve two-marker questions from the previous years papers, 25 in all.Day 3, session 1: Dual Nature of radiation and matter (4 hours)Start with De Broglie hypothesis [math]( \lambda = h/p)[/math]. Following questions are generally asked based on this formula.De Broglie wavelength associated with a particle having certain momentum [math](h/p)[/math], certain kinetic energy [math]( \frac h{\sqrt{2Km}})[/math], thermal neutron [math]( \frac h{\sqrt{3K_B m}})[/math].De Broglie wavelength associated with a charge q accelerated through V volt [math](\frac h{\sqrt{2qVm}})[/math], electron associated through V volt [math](\frac{1.227}{\sqrt V} nm)[/math], of electron in nth Bohr’s orbit [math](2\pi r_n = n\lambda \Rightarrow \lambda = \frac{2\pi r_n}n)[/math].Graph of De Broglie wavelength of a charge q versus [math]\frac 1{\sqrt V}[/math]. see what you can find from the slope of this graph.Principle behind Davisson and Germer experiment, how the experiment confirms De Broglie hypothesis. No experimental details.Solved examples 11.5, 6, 7. Exercises No. 11.13, 16, 17, 18.Photon picture of electromagnetic radiation(page 396 NCERT), definition of intensity in photon picture of light ( Intensity is related to number of photons passing through unit area per unit time).Three main observations of experiment on photoelectric effect, their explanations and how the wave theory fails to explain them.Figure 11.3, 4 and 11.5. Make three graphs corresponding to figure 5 (listed below) and see how you can find the value of h, \phi_0 and \nu_0 or \lambda_0 from the graph.[math]Km = h\nu - \phi_0[/math]; Gradient h, intercept [math]\phi_0, [/math][math]V_0 = \frac h{e} \nu - \frac{\phi_0}e[/math]; Gradient [math]\frac he,[/math] intercept [math]\frac{\phi_0}e[/math][math]v^2_m = \frac {2h}m \nu - \frac{2\phi_0}m[/math]; Gradient [math]\frac {2h}m[/math], intercept [math]\frac{2\phi_0}m[/math]Solve the questions from 5 years’ papers related to this chapter. Leave NCERT questions.Day 3, session 2: Electromagnetic waves (4 hours)By the time you are certainly bored of this modern physics stuff. Take a lighter chapter for entertainment.Production, detection, application and range of frequencies of [math]micro[/math] (why used in RADAR), UV, X and gamma (table 8.1)Average magnetic energy density (\frac{B^2}{2\mu_0}, electric energy density (\frac 12 \epsilon_0 E^2). Show that both are equal by using E = Bc and c =\frac 1{\sqrt{\mu_0 epsilon_0}}. Intensity of em wave (c\epsilon_0 E^2). Finding amplitude of E and B, wavelength, frequency, direction of propagation and speed of wave from the equation of electromagnetic wave ( exercise 8.1, there is a misprinting in the question - it should be 10^8 instead of 10^6)Displacement current: Inconsistency (anomaly) in Ampere’s circuital law, How Maxwell removed the inconsistency, Important implications (consequences) of the displacement current / Maxwell’s discovery/missing term. Click on the screen shot given below to make it readable.The answer is getting too big and unmanageable. Keeping it short, I would suggest that in the remaining time you undertake the chapters in the following order.Wave optics: It broadly has four part. Huygens construction, interference, diffraction polarisation and a bit of resolving power. This chapter appears complicated but actually this is a small and easy one one. Must do all the solved example of NCERT, specially 10.4.Semiconductor: Have to read the complete chapter but questions on formation of junction, zener diode, LED, amplifier are more often asked than others.Electromagnetic induction: Questions on motional emf, Lenz’s law, self and mutual induction are generally asked. Do all the solved examples.AC: Again a very small chapter. A numerical on LCR circuit is most probable. Graph of current amplitude versus frequency is important. Analytical parts of LCR circuit, LC parallel circuit and quality factor are not in syllabus. Exercises 7.11, 18, 20, 25 are important.Electrostatics, Current electricity, Magnetism and Ray optics: There is no limit on the types of questions that can be asked. Hence concentrate on derivations. However solve from the last five years papers, the questions on capacitors, dipoles, potentiometer, meter bridge, Kirchhoff’s rules, cyclotron, earth’s magnetic field, refraction through spherical surfaces, lens makers’ formula and prism.ALL THE BESTAnswers to some relevant questions can be found here:In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band?What happens when the distance between a single source of light and the plane of a double slit decreases?Answer the question in simple words: A current carrying a circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loop turns around itself (i.e. turns about the vertical axis)?What is a magnetic field at the centre of a circle when charge q coulomb moves in a circle at n revolutions per second and the radius of a circle is R?What is the ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two fringes from the centre?If ratio of frequencies in two Bohr orbits of a hydrogen atom is 1:27, what is the ratio of radii of these orbits?A charge particle can't be held in a stable equilibrium by electrostatic force alone, why?A 12.5 eV electron beam is used to excite a gaseous hydrogen atom at room temperature. Can you determine the wavelength and corresponding series of the lines emitted?In a LCR circuit, if R represents an electric bulb and the frequency of the supply is doubled, how should the values of L and C be changed so that the glow in the bulb remains unchanged?If a bar magnet is replaced by a combination of two similar bar magnets placed over each other, how will the time period vary?What is relation between speed of object and speed of image for a spherical mirror?If two unlike capacitors of different potentials and charge are joined in parallel, what happens to their potential difference? How are their charges distributed? Is the energy of the system affected?What is meant by the statement that the electric field of a point charge has spherical symmetry whereas that of an electric dipole is cylindrically s?If a dielectric is placed inside a parallel plate capacitor after the battery is removed, how is voltage, charge on each plate & capacitance affected?How is the concept of displacement current associate symmetry in the behaviour of electric and magnetic fields?

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