6.32) A spherical quantum dot embedded in silicon dioxide (which has a dielectric constant of 4.5)...
1) A silicon cantilever beam with mass = 4 x 10-10 Kg has a spring constant of 31 N/m. Calculate the natural frequency of the beam in Hz. Assume no damping. 2) An atom in a lattice has a resonance frequency of 9.2 THz. According to quantum mechanics, what is the lowest amount of energy this oscillator can have? Express answer in J.
A spherical capacitor has a spherical inner plate with radius a
and outer plate with radius b. The charge on the inner plate is +Q
and on the outer plate it is -Q. We have filled a cone shaped
region of angle θ (0 ≤ θ ≤ π) with a dielectric with constant κ.
The dielectric fills the entire volume between the two spheres
inside the cone. You may neglect any fringing effects between the
dielectric and the vacuum (dielectric...
4. Through-silicon-via (TSV) has been widely used in electronics, which is a vertical metal via that passes completely through a silicon substrate. Consider a metal TSV embedded in the silicon substrate. The TSV is made from steel and copper, which have the thermal conductivities of ksteel 50 Wm K, and k-400 Wm K. The silicon has a thermal conductivity of ks-100 Wm K-1. The analysis of thermal transport in the TSV-Si composite can start from its unit cell due to...
Which of the following elements has at least one electron in which the magnetic quantum number (m) equals -3? Neodymium Iridium Cadmium Cobalt Darmstadtium Selenium Silicon Carbon Q: What is true of the most stable resonance structure for CH2CH2? Carbon is sp3 hybridized Carbon bears a lone pair There is one pi bond between the two carbon atoms The bond order between the carbon-carbon bond is 2 Hydrogen bears a lone pair Carbon is sp2 hybridized The molecular geometry around...
2. A1 cm tall Christmas light is 2 cm from a spherical, reflecting ornament which has a diameter d= 8 cm. (a) (5 points) Draw the ray diagram for this setup. (b) (5 points) What is the distance from the Christmas light to its image in cm? (c) (5 points) How tall does the image appear to be?
Assignment 4 Application of Kinetics 1. A reaction AB has rate constant of 10.018 L/mol min) How long does it take for the concentration of A to decrease to to th of its initial concentration of 2.5m? 14 2. The half-life for the decay of C is 5730 years. it emits ß-rays with an energy of 0.16 MeV. A sa. of wood has a72% of its 14 C left. What is the sample age of this word ? 3. when...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate in 3D, one can always define a set of angular momentum operators J. Jy, J., often collectively written as a vector J. They must satisfy the commutation relations (, ] = ihſ, , Îu] = ihſ, J., ſu] = ihỈy. (1) In a more condensed notation, we may write [1,1]] = Žiheikh, i, j= 1,2,3 k=1 Here we've used the Levi-Civita symbol, defined as...
An undamped 2.19 kg horizontal spring oscillator has a spring constant of 34.5 Nm. While oscillating, it is found to have a speed of 2.50 m/s as it passes through its equilibrium position. What is its amplitude of oscillation? amplitude of oscillation: What is the oscillator's total mechanical energy as it passes through a position that is 0.584 of the amplitude away from the equilibrium position? total mechanical energy:
An undamped 2.87 kg horizontal spring oscillator has a spring constant of 26.5 N/m. While oscillating, it is found to have a speed of 3.02 m/s as it passes through its equilibrium position. What is its amplitude of oscillation? amplitude of oscillation: What is the oscillator's total mechanical energy as it passes through a position that is 0.629 of the amplitude away from the equilibrium position? total mechanical energy:
An undamped 1.02-kg horizontal spring oscillator has a spring constant of 29.9 N/m. While oscillating, it is found to have a speed of 2.21 m/s as it passes through its equilibrium position. What is its amplitude of oscillation? What is the oscillator\'s total mechanical energy as it passes through a position that is 0.701 of the amplitude away from the equilibrium position?