Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Question
Chapter 38, Problem 70P
To determine
The rms energy of a Fermi distribution and compare it with average and reason for their difference.
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b) Find Ef in terms of N and V.e) What is the pressure at tje Fermi gas at T=0 K. ?
Silicon is doped with phosphorus atoms (column V of Mendeleev table) with a concentration of
1018 cm-3
a- What is, at 27 °C, the electron density in doped Si. Use this result to derive the hole density.
Which type of semiconductor is obtained?
b- Calculate, at 27 °C, the position of the Fermi level EF and plot the band diagram.
Pressure and bulk modulus of an electron gas. (a) Derive a relation connecting
the
pressure
and volume of an electron gas at 0 K. Hint: Use the result of Problem
1 and the relation between er and electron concentration. The result may be writ-
ten as p =(U/V). (b) Show that the bulk modulus B = –V(dp/əV) of an electron
gas at 0 K is B = 5p/3 = 10U/9V. (c) Estimate for potassium, using Table 1, the
value of the electron gas contribution to B.
Chapter 38 Solutions
Physics for Scientists and Engineers
Ch. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10P
Ch. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46PCh. 38 - Prob. 47PCh. 38 - Prob. 48PCh. 38 - Prob. 49PCh. 38 - Prob. 50PCh. 38 - Prob. 51PCh. 38 - Prob. 52PCh. 38 - Prob. 53PCh. 38 - Prob. 54PCh. 38 - Prob. 55PCh. 38 - Prob. 56PCh. 38 - Prob. 57PCh. 38 - Prob. 58PCh. 38 - Prob. 59PCh. 38 - Prob. 60PCh. 38 - Prob. 61PCh. 38 - Prob. 62PCh. 38 - Prob. 63PCh. 38 - Prob. 64PCh. 38 - Prob. 65PCh. 38 - Prob. 66PCh. 38 - Prob. 67PCh. 38 - Prob. 68PCh. 38 - Prob. 69PCh. 38 - Prob. 70PCh. 38 - Prob. 71PCh. 38 - Prob. 72PCh. 38 - Prob. 73PCh. 38 - Prob. 74PCh. 38 - Prob. 75PCh. 38 - Prob. 76P
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- A state 63 meV above the Fermi level has a probability of occupancy of 0.090.What is the probability of occupancy for a state 63 meV below the Fermi level?arrow_forwardQ5/ (a) If the Fermi energy of copper at 300K is 7.05 eV, calculate the probability that a state with energy equal to 99.2 % of the Fermi energy is occupied. (b) What is the Debye frequency of copper, if it has Tp of 315K, and find the Debye specific heat capacity at 10K and at 30OK.arrow_forwardA silicon ingot is stained with ( Nd = 10 ^ 16atom / cm ^ 3) ars enic atoms. A) Get the density of the carrier s and b) Get the Fermi level at r oom temperature T = 300k?arrow_forward
- Q3/ An experiment was conducted to find the relationship between the specific heat of potassium metal and the temperature, and it was found that this relationship takes the following formula at low temperatures 2.08 +2.57 T2 What is the value of each of: (1) the fermi temperature of potassium? (b) Debye temperature of potassium? Note that specific heat is measured in units of mj / mol / K.arrow_forwardd) Use the Fermi distribution function to obtain the value of ?(?) for ? − ?? = 0.01?? at 200Karrow_forward(a) Obtain total partition function for an Ideal di-atomic gas and use it to drive the expression of specific heatarrow_forward
- Let's look at a copper crystal, where each copper atom donates one conduction electron to the crystal. a) Use the free electron model to determine the prediction for copper fermi energy EF, fermi temperature TF and degeneration pressure Pdeg (at temperature T = 0 K). b) Further calculate the contribution of the degeneration pressure to the isothermal compression coefficient of copper. B = -V др (SP) T c) Finally, determine the model prediction for the electronic molar specific heat capacity Cy . The empirical form for this is Cy = yT and the experimentally determined value for copper is Y = 0.695 mJ mol-¹ k-². = Compare this numerical value with your resultarrow_forwardTo obtain a more clearly defined picture of the FermiDirac distribution, consider a system of 20 FermiDirac particles sharing 94 units of energy. By drawing diagrams like Figure P10.11, show that there are nine different microstates. Using Equation 10.2, calculate and plot the average number of particles in each energy level from 0 to 14E. Locate the Fermi energy at 0 K on your plot from the fact that electrons at 0 K fill all the levels consecutively up to the Fermi energy. (At 0 K the system no longer has 94 units of energy, but has the minimum amount of 90E.) 1 Microstate8 others? One of the nine equally probable microstates for 20 FD particles with a total energy of 94E.arrow_forwardThe mean flee path for helium at a certain temperature and pressure is 2.10107 m. The radius of a helium atom can be taken as 1.101011 m. What is the measure of the density of helium under those conditions (a) in molecules per cubic meter and (b) in moles per cubic meter? `arrow_forward
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