9B. a) Do particles of matter have wave properties? b). Who was the first physicist to give a convincing answer to the question? c). As the speed of a particle increases, does its associated wavelength increase or decrease? Your answer

L. An electron is confined in a cubical box of side 1Å. (i) Find its lowest energy (ii) what is the temperature at which the average ofthe molecule.ofa perfect gas would be equal to the lowest energy of the clectron (k =1.38×10-23 JI/K)?

a. Conceptually, discuss the particle-wave duality of light. Discuss the implications of this in combination with the de Broglie (pronounced “de Broy”) equation. b. The electron of a hydrogen atom is usually no further than 1.0 Å from the proton. We can therefore say the upper limit of the radius of an isolated hydrogen atom is roughly 1.0 Å. How does the de Broglie wavelength of the electron compare to this radius? (The velocity of an electron in the first principal energy level is about 2.2 x 106 m/s). Explain why wave-particle duality is so important for quantum mechanics, yet not required in macroscopic systems that are well described by classical mechanics. c. Comment as to whether neutrons with velocity 4.14 x 103 m/s may be used to determine structures of molecules in a diffraction-based experiment. You may consider the relevant distance between atoms in molecules to be on the order of 1 Å.

A sodium gas is contained in a cubical container (T=250 K) with one side measuring 25.0 m. a.) What is the minimum uncertainty in momentum components of the sodium atoms? b.) What is the minimum uncertainty in velocity components? c.) Find the ratio of uncertainties in your answer in letter b, to the mean speed of an atom in each direction.

When light of wavelength 310 nm is incident on a metal surface, electrons are ejected with a kinetic energy of 1.0 eV. a. What is the work function (binding energy) of this metal (in eV)? b. What is the cutoff wavelength of light (in nm) that can eject electrons? Will photons with wavelength 544 nm eject electrons? Explain your reasoning. c. Determine the wavelength of light (in nm) that should be used to double the kinetic energy of the electrons ejected from this surface.

As shown the energy levels of a hypothetical atom.a. What minimum kinetic energy (in eV) must an electron have to collisionally excite this atom and cause the emission of a 620 nm photon? Explain.b. Can an electron with K = 6 eV cause the emission of 620 nm light from this atom? If so, what is the final kinetic energy of the electron? If not, why not?c. Can a 6 eV photon cause the emission of 620 nm light from this atom? Why or why not?d. Can a 7 eV photon cause the emission of 620 nm light from this atom? Why or why not?

a. How much energy is required to ionize a hydrogen atom containing an electron in the n=4 level? b. What wavelength of light contains enough energy in a single photon to ionize a hydrogen atom?

D1. Consider a hydrogen atom that is initially in the 4p state. Determine the following: (a) the energy of the atom in this state (ignore hyperfine effects), and (b) the most orbital angular momentum that could be added to the atom without changing its principal quantum number and the spectroscopic notation for this new state (i.e. does it become 3s or 5p or...?) (based on Q61)

The mass of an electron is 9.11  10-31 kg.A.) If the wavelength of an electron is 5.02  10-7 m, how fast is it moving?  B.) If an electron has a speed equal to 4.30  106 m/s, what is its wavelength?

6. An electron in hydrogen atom is in initial state p(r, 0) = A(2µ100 + ¡Þ210 + 4Þ21–1 – 2i4211) where ynim are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? c. Write the state p(r, t) at time t, using energy eigenvalues as En = d. Find the expectation value of L in the state (r,t e. Find the expectation values of Lx and Ly in the state (r, t f. If measurement of L, led to the value -ħ what will be results of measurement of energy and the square of total orbital momentum immediately afterwards and what are their probabilities? hw n2