A 1.00 kg weight is traveling at a constant velocity of 10.0 ms-1, in a cubic room 3.00 m on an edge.(a). Determine the sum of the squares of its three quantum numbers.(b). What would be the ground state energy for this weight?

Consider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction ψn. (a) Without evaluating any integrals, explain why ⟨x⟩ = L/2. (b) Without evaluating any integrals, explain why ⟨px⟩ = 0. (c) Derive an expression for ⟨x2⟩ (the necessary integrals will be found in the Resource section). (d) For a particle in a box the energy is given by En = n2h2/8mL2 and, because the potential energy is zero, all of this energy is kinetic. Use this observation and, without evaluating any integrals, explain why <p2x> = n2h2/4L2.

(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3.

Suppose that 1.0 mol of perfect gas molecules all occupy the lowest energy level of a cubic box. (a) How much work must be done to change the volume of the box by ΔV? (b) Would the work be different if the molecules all occupied a state n ≠ 1? (c) What is the relevance of this discussion to the expression for the expansion work discussed in Topic 2A? (d) Can you identify a distinction between adiabatic and isothermal expansion?

3. ^14N^16O (the superscripts represent the atomic mass number)  (a) NO molecules rotate at an angular velocity of 2.01x10^12 rev/s, at the quantized rotational state with the rotational quantum number J of 3. Calculate the bond length of NO molecules. (b) Can NO molecules rotate under light irradiation? Explain your answer. (c) Calculate the effective force constant of the vibrational mode of NO at a frequency of 5.63x10^13 Hz measured by the infrared absorption spectrum. (d) NO has a bond energy of 6.29 eV. Applying the parabolic approximation to estimate the longest distance in which N and O atoms can be stretched before the dissociation of the molecular bond

A glow worm of mass 5.0 g emits red light (650nm) with a power of 0.10W entirely in the backward direction. To what speed will it have accelerated after 10y if released into free space and assumed to live? Energy emitted = P(W)-At(s). Assume the conservation of linear momentum, which means that the loss of a photon imparts an equivalent momentum in the opposite direction. total energy The total momentum imparted to the glow-worm: p = Npphoton where energy/photon x= 650nm N = Energy emitted p = mv Energyphoton V= = { PglowwormN Pphoton N = # of photons = Pphoton = momentum/photon 5g=00005kg = (mv) glowworm At =10yrs => At-see Total Energy = Pat energy/photon = (E=hr) = hec Pphoton = 12 숫

Consider a collection of 10,000 atoms of rubidium-87, confined inside a box of volume (10-5 m)3. Suppose that T = 0.9Tc. How many atoms are in the ground state? How close is the chemical potential to the ground-state energy? How many atoms are in each of the (threefold-degenerate) first excited states?

How to slove this solution

8C.4 (a) the moment of inertia of a CH4 molecule is 5.27 x 10^-47 kg m^2. What is the minimum energy needed to start it rotating? 8C.5 (a) use the data in 8C.4 (a) to calculate the energy needed excite a CH4 molecule from a state with l=1 to a state with l=2

A nitrogen molecule is confined in a cubic box of volume 1.00 m3. (i) Assuming that the molecule has an energy equal to 3/2kT at T = 300 K, what is the value of n = (nx2 + ny2 + nz2)1/2 for this molecule? (ii) What is the energy separation between the levels n and n + 1? (iii) What is the de Broglie wavelength of the molecule?