V(x) = 1½ kx² + yx³ + ¼ 1½ бx² 4 Your energy should be expressed in terms of the parameters k, y, &, Planck's constant h (or h), and the reduced mass, μ.
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Use perturbation theory to calculate the first-order correction to the ground state energy of
an anharmonic oscillator whose potential energy is given by,
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- 3. The equation 1.45 in our textbook says that the de Broglie wavelength as a function of temperature is given by 1 Assuming the accepted accuracy for h, R, and m are very high, what is the V3MRT maximum uncertainty in the de Broglie wavelength if AT is the uncertainty in temperature?Calculate the wavelength of electrons accelerated through 1742 V. (electron mass m = 9.1 x 10-31 Kg, electronic charge e=1.6 x 10-19 C and the Planck constant h=6.6 x 10-34 Js) Round off the answer to 2 decimal places and write answers as power of 10.Find Relative error for the find planck constant: h = (1.60217662 x 10^-19)(4.1628 10^-6 ±1.25718 10^-7)/(299792458)
- The kilogram has been redefined based on Planck's constant (h) and a sphere of pure crystalline silicon: 8AsiVsphere Msphere = 2h 13 ст-а? The terms (with their relative uncertainties) are: (1) Planck's constant h (zero uncertainty as it is defined exactly); (2) the bracketed term including accurately known Rydberg constant R, speed of light c, mass of electron (me), and fine structure constant a, with a combined uncertainty of +4.7 × 10-8%; (3) atomic mass Asi for the 28 Si-enriched silicon (+5.4 x 10-7%); (4) volume of the Si sphere (+2.0 × 10-6%) and (5) crystal lattice parameter I (+1.84 x 10-7%). There are exactly eight atoms per unit cell in the sphere. Compute the relative uncertainty of myphere- To find the uncertainty of l, use the function y = x“, for which the uncertainty is propagated using %e, = a(%e,). relative uncertainty of msphere: % The mass of the sphere of pure silicon (999.698 336 5 g) must also be corrected for defects in the crystal lattice ( mdefects = 3.8…(a) What is a.m.u? Express 1 a.m.u. in MeV. (b) Write the approximate mass of a proton, neutron and electron in a.m.u.Calculate the effective mass m* of electron with the momentum k G/2 in a weak periodic potential U(x) = 2Uo cos(27x/a) for which the energy spectrum E(k) is given by Eq. (1.3.22) of Lect. 4. The mass m* is defined by the behavior of E(k) at k G/2: h?q? G G k « 2 E(k) = Em 2m** 2 Can m* be smaller or larger than the free electron mass?
- Calcúlate the uncertainty for momentum p, when the mass of the object is 15.0 (+-) 0.2kg with a velocity of 7.0 (+-) 0.5m/s. What is the uncertainty percentage of the momentum?8πhy3 dv (a) Express the Planck radiation formula, Edv = c3 ehv/kT-1' terms of λ (and dλ), namely Edλ. (b) Solved=0 for λ = Amax in to determine the value of maxT in m-K, where max is the wavelength at which the blackbody spectrum has its maximum value at a given temperature T.Suppose that Vsound = (32 ± 7) x 101 m/s and that we want to find the temperature in Kalvin by using the following formula: T = (50und)2. Find the value of the 20 Temperature in degree Celsius (°C) and his uncertainty. Thank you
- Lunar astronauts placed a series of cube reflectors on the Moon as part of an experiment to mea- sure the distance to the Moon with hyperaccuracy. Lasers were fired from an observatory in West Texas toward the Moon; they reflected off these cubes and returned to Earth. The time of arrival was measured by astronomers at the observatory. If the time for the round trip could be measured with an accuracy of 0.1 nanoseconds, what was the uncertainty in the measured distance to the Moon. Given that the semi-major axis of the Moon’s orbit is 3.84 x 108 km, what is the percent accuracy of these measurements?An angle is measured to be 29.0±0.4deg. What is the absolute uncertainty in the sine of the angle? What is the absolute uncertainty in the cosine of the angle?Find the uncertainty in kinetic energy. Kinetic energy depends on mass and velocity according to this function E(m,v) = 1/2 m v. Your measured mass and velocity have the following Sm = uncertainties = 1.33 kg and SV = 2.15 m/s. What is the uncertainty in energy, SE , if the measured mass, m = 2.47 kg and the measured velocity, v = -31.26 m/s?
