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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- An angle is measured to be 0.34±0.04rad. What is the absolute uncertainty in the sine of the angle?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?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.
- 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?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 youFind 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?
- Problem-1: An asteroid is hurtling toward earth at 150,000“. The temperature of the asteroid is about 100 K, meaning that its peak emission is 2 = 29 µm. The speed of light is c = 3E[8]. a) What is the wavelength of light that we receive from the asteroid? (Answer: 2.89855E[-05] m)4. In Section 1.3 we used dimensional analysis to show that the size of a hydrogen atom can be understood by assuming that the electron in the atom is wave-like and non-relativistic. In this problem we show that, if we assume the electron in the atom is a classical electron described by the theory of relativity, dimensional analysis gives an atomic size which is four orders of magnitude too small. Consider a relativistic, classical theory of an electron moving in the Coulomb potential of a proton. Such a theory only involves three physical constants: m, /4mc9, and e, the maximum velocity in relativity. Show that it is possible to construct a length from these three physical constants, but show that it too small to characterize the size of the atom.2.3. Find the de Broglie wavelength of (a) an electron, and (b) a proton with speeds of 5 × 106 m/s and compare with the radius of the hydrogen atom, ao. Would either of these particles behave like a wave inside the H atom?
- With what speed would a rock of mass 49.0 g have to be thrown if it were to have a wavelength of 4.33 × 10¬34 m? Planck's constant is 6.63 × 10¬34 J . s. Answer in units of m/s.snipImagine another universe in which the value of Planck’s con- stant is 0.0663 J s, but in which the physical laws and all other physical constants are the same as in our universe. In this universe, two phys- ics students are playing catch. They are 12 m apart, and one throws a 0.25 kg ball directly toward the other with a speed of 6.0 m/s. (a) What is the uncertainty in the ball’s horizontal momentum, in a direction per- pendicular to that in which it is being thrown, if the student throwing the ball knows that it is located within a cube with volume 125 cm3 at the time she throws it? (b) By what horizontal distance could the ball miss the second students?
