7.1. Given the following values for P₁, P2, and I, AL₁, calculate AH₂: (a) P₁(0, 0, 2), P₂(4, 2, 0), 2ra-A-m; (b) P₁(0, 2, 0), P₂(4, 2, 3), 27a-A-m; (c) P₁(1, 2, 3), P₂(-3,-1, 2), 2(-a, +a, +2a)A-m.
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- A hydrogen atom (with the Bohr radius of half an angstrom) is situated between two metal plates 1 mm apart, which are connected to opposite terminals of a 500 V battery. What fraction of the atomic radius does the separation distance d amount to, roughly? Estimate the voltage you would need with this apparatus to ionize the atom.Consider an isolated carbon atom being held in its equilibrium lattice site position by the mutual interaction with the neighboring atoms. If the spring constant driving the carbon atom back into its equilibrium lattice site is 21.71 N/m, what is the frequency of oscillation? The atomic mass of carbon is given in the periodic table. Give your answers in units of 1012 rad/s with 2 digits precision, rounding off to two decimal places, i.e. the nearest hundredths. (time budget 6min)3.17 Figure P3.17 shows the parabolic E versus k relationship in the valence band for a hole in two particular semiconductor materials. Determine the effective mass (in units of the free electron mass) of the two holes. -0.08 Ey Ey-0.025 Ev-0.3 E(eV)+ 0k (ů) 0.08 Figure P3.17 | Figure for Problem 3.17.
- The Lennard-Jones potential, (E = 48[-(0/r)6+ (o/r)¹2]), is a good approximation that describes realistic potential energy of 2 atoms, where o is collision distance and ris the distance between two atoms. Explain the physical meaning when (1) r = o and (ii) ro=1.1220.Given the work functions for some metals:- Aluminum-D4.08eV, Beryllium=5.0eV, Cadmium%3D4.07eV, Calcium32.9eV, Carbon3D4.81eV, Cesium=2.1eV, Cobalt=5.0eV, Copper3D4.7eV, Gold=5.1eV, Iron%3D4.5eV, Lead%-4.14eV, Magnesium=3.68€V, Mercury=D4.5eV, Nickel=5.01eV, Niobium=4.3eV, Platinum=6.35eV, Potassium=2.3eV, Selenium=5.11eV, Silver=4.73eV, Sodium=2.28eV, Uranium3D3.6eV, and Zinc3D 4.3eV. If you shine light with a wavelength of 153 nm on Potassium, what is the velocity of the electrons being emitted. Provide your answer in units of 105 m/s and round it off to two decimal places, i.e. the nearest hundredths.(a) How many silicon atoms are there in each unit cell? (b) How many silicon atoms are there in one cubic centimeter? (c) Knowing that the length of a side of the unit cell (the silicon lattice constant) is 5.43 Å, Si atomic weight is 28.1, and the Avogdaro's number is 6.02 × 10²3 atoms/mole, find the silicon density in g/cm³.
- if the chlorine molecule at 290K were to rotate at the angular frequency predicted by the equipartition theorem what would be the average centipital force ? ( the atoms of Cl are 2 x 10-10 m apart and the mass of the chlorine atom 35.45 a.m.u )from 7/2 to TI from (–10) to (10) (2a) The average of f(x) = cos(3x) (2b) The average of f(x) = x² (2c) The average of f(x) = 2x sin(x) (2d) The average of f(x) = 3x from 0 to ↑ %3D from (-3) to (3)If the radius of a calcium ion is 0.27 nm, how much energy does it take to singly ionize it? Give your answer in electron-volts (eV) with precision 0.1 eV. Give your answer to 2 significant digits.
- Given: R is the midpoint of QS, ZRPQ =ZRTS prove: APQR = ATSR P.5-1. The electron-neutral collision cross section for 2-eV electrons in He is about 6rab, where ao =0.53 x 10 cm is the radius of the first Bohr orbit of the hydrogen atom. A positive column with no magnetic feld has p = 1 Torr of He (at room temperature) and KT, = 2 eV. %3D (a) Compute the electron diffusion coefficient in m/sec, assuming that o averaged over the velocity distribution is equal to ou for 2-eV electrons.. (b) If the current density along column is 2 kA/m and the plasma density is 10 m, what is the electric field along the colurnn?If A =〖yz〗^2 i-3xz^2j +2xyz k, B = 3xi +4zj -xyk and ∅= xyz, findd^2/dxdy [Ax (B.∅)] at P(1, 1, 1)