Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 5, Problem 5.22P
To determine
Predict the slope of the graph from Moseley's formula and check whether the Moseley's observation data for different anode material bear out our prediction.
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Ex 4.11
Consider silicon at T =
300 K. Calculate the thermal-equilibrium electron and
hole concentrations for impurity concentrations of (a) Na = 4 X 1016 cm,
Na = 8 X 1015 cm-3 and (b) Na = Na = 3 X 1015 cm-3.
Problem 4.45 What is the probability that an electron in the ground state of hydro-
gen will be found inside the nucleus?
(a) First calculate the exact answer, assuming the wave function (Equation 4.80)
is correct all the way down to r = 0. Let b be the radius of the nucleus.
(b) Expand your result as a power series in the small number € = 2b/a, and
show that the lowest-order term is the cubic: P≈ (4/3)(b/a)³. This should
be a suitable approximation, provided that b
Consider N identical harmonic oscillators (as in the Einstein floor). Permissible Energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on.
A) Calculating the selection function of a single harmonic oscillator. What is the division of N oscillators?
B) Obtain the average energy of N oscillators at temperature T from the partition function.
C) Calculate this capacity and T-> 0 and At T-> infinity limits, what will the heat capacity be? Are these results consistent with the experiment? Why? What is the correct theory about this?
D) Find the Helmholtz free energy from this system.
E) Derive the expression that gives the entropy of this system for the temperature.
Chapter 5 Solutions
Modern Physics For Scientists And Engineers
Ch. 5 - Prob. 5.1PCh. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Prob. 5.17PCh. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Prob. 5.26PCh. 5 - Prob. 5.27P
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- Problem 1: Estimate the probability that a hydrogen atom at room temperature is in one of its first excited states (relative to the probability of being in the ground state). Don't forget to take degeneracy into account. Then repeat the calculation for a hydrogen atom in the atmosphere of the star y UMa, whose surface temperature is approximately 9500K.arrow_forwardFor KMnF 3 shown in Fig. 9.9, it becomes an antifoerromagnet at low temperature.Namely the magnetic moment of the Mn in the sublattice A and B pointing to the oppositedirection. Now assign the angular momentum on the A and B sublattice as J and –J respectively,a) Derive the expression of the cross-section for magnetic diffractionb) Find out the first three non-zero magnetic Bragg peaksc) Derive the expression of the cross-section for nuclear (crystalline) diffractionarrow_forwardQ.2: A 5 mA diode is connected in series with a 100 ohms resistance and a DC voltage source derived from the output of a half-wave rectifier (HWR). The ac voltage driving the rectifier is of amplitude 35 volts. (a) What will be the DC current through the diode (use exponential l-V relation for the diode, and iteration method)? (b) What will be the ac resistance of the diode?arrow_forward
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- A particle with a size just below r* is unstable but a particle with a size 2) just above r* is stable. What comments would you make on this statement? If you agree then, why are the particles just above (very little bigger than r*) a critical size r* thermodynamically stable even though the energy (Gibbs free energy) is positive. a) A 4G, surface energy 4xr'y AG Volume free energy Excess free energy AG. b) Why the free energy vs particle radius curves for homogeneous and heterogeneous nucleation differs. CAG, AG AG JAGeter AGomaarrow_forwardThe Einstein model for a solid assumes the system consists of 3N independent simple harmonic oscillators with frequencies &. Within these assumptions, the heat capacity at constant volume as: Cv=3Nk() (-1)² ² Complete the table for the molar heat capacity at various temperatures under either the Einstein model or high-temperature limit. You might like to use the Wolfram Alpha calculator to do the numerical calculations more easily. Use k-0.695 cm /K. High temperature limit value of molar heat capacity of metal is T 1 K 10 K 50 K -1 Einstein, = 100 cm Einstein, : = 500 cm 1.4021 3.8991 100 K 500 K 2.434E-4 1000 K 6.1499 2434E-4 kJ/mol.arrow_forwardProblem # 2. In the two-level system, estimate the emission line full width at half maximum (FWHM) for spontaneous emission at 650 nm if the spontaneous radiative lifetime of the upper state is about 3,000 nanoseconds.arrow_forward
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