3. (a) What is the energy AND magnitude of angular momentum for a particle on a sphere if the particle is an electron, the sphere has aradius of 600 pm, and the quantum numbers for the state of the particle arel= 3 and m =+1 Report answers in Si units. (b) What choice of m; would place LESS orbital motion in the xy-plane?

An electron is confined to a one-dimensional region in which its ground-state (n = 1) energy is 1.45 eV. (a) What is the length L of the region? nm(b) What energy input is required to promote the electron to its first excited state? eV

Calculate the de Broglie wavelength for: a) An electron (9.11 x 10-31) moving at 1 x 106 m/s b) A neutron (1.67 x 10-27 kg) moving at 2.6 x 104 m/s Both particles approach a potential barrier (U = 5 eV) 0.26 nm wide. Calculate the transmittance coefficient for each particle. %3D

An electron in a multielectron atom has ML=+4 . For this electron, what are (a) the value of , (b) the smallest possible value of n, and (c) the number of possible values of ms?

3. Particle in a 2D Box. A quantum mechanical particle is confined in side a square 2D box, with side length L. Inside the box V=0 and outside the box V=infinity. Let the wave function to be (x,y). (a) write down the Schrodinger equation of (x,y). (b) Use the separation of variable method solve (x,y) (let the quantum numbers to be nx and ny.) (c) What is the energy for the state (nx, ny)? (d) What is the probability density p(x,y) for the state nx=3 and ny=3? Sketch this p(x,y) in a square.

In the Bohr model of the atom, we assume that nanoscale particles behave according to classical physics (This assumption is not entirely justified, but does work surprisingly well). In this model, an electron (mass m = 9.11 x 10-³1 kg) orbits a nucleus at a distance that depends on the principal quantum number of the electron (1s orbital, 2s orbital, etc) and the composition of the nucleus. If the electron orbits at a distance of 9.90 x 10-¹1 m due to a Coulomb force of 2.35 x 10-8 N, how many revolutions per second does the electron make? 2.569

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(a) A hydrogen atom has its electron in the n = 6 level. The radius of the electron's orbit in the Bohr model is 1.905 nm. Find the de Broglie wavelength of the electron under these circumstances. m (b) What is the momentum, mv, of the electron in its orbit? kg-m/s

What wavelength of light is emitted by a hydrogen atom in which an electron makes a transition from the n = 8 to the n = 5 state? Enter this wavelength expressed in nanometers. 1 nm = 1 x 10-9 m  Assume the Bohr model.