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Chapter 41: Q53P (page 1275)

At what pressure, in atmospheres, would the number of molecules per unit volume in an ideal gas be equal to the number density of the conduction electrons in copper, with both gas and copper at temperature T =300K?

Short Answer

Expert verified

The pressure value that would give the number of molecules per unit volume in an ideal gas equal to the number density of conduction electrons in copper is 3.49×103atm.

Step by step solution

01

The given data

a) The number of conduction electrons in copper,n/V=8.43×1028m-3

b) The temperature value, T =300 K

02

Understanding the concept of ideal gas equation

The equation that relates the characteristic properties of an ideal gas is known as Ideal Gas Equation. The ideal gas equation can be given as-

PV=nkT

Here P is the pressure,V is the volume, n id the number of moles and k is the Boltzmann constant.

03

Calculation of the pressure

Using the given condition and data in equation, we can get the value of the pressure in atmospheres as follows:

P=nkTV=8.43×1028m-31.38×10-23J/K300K=3.49×108Pa=3.49×103atm

Hence, the value of the pressure is 3.49×103atm.

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Most popular questions from this chapter

Figure 41-21 shows three leveled levels in a band and also the Fermi level for the material. The temperature is 0K. Rank the three levels according to the probability of occupation, greatest first if the temperature is (a) 0K and (b) 1000K. (c) At the latter temperature, rank the levels according to the density of states N(E) there, greatest first.

Show that, atT=0K , the average energyEavg of the conduction electrons in a metal is equal to35EF . (Hint:By definition of averageEavg=(1/n)∫EN0(E)dE , where nis the number density of charge carriers.)

Show that P(E), the occupancy probability in Eq. 41-6, is symmetrical about the value of the Fermi energy; that is, show that P(EF+ΔE)+P(EF-ΔE)=1.

A sample of a certain metal has a volume of 4.0×10-5m3. The metal has a density of 9.0 g/cm3and a molar mass of 60 g/mol. The atoms are bivalent. How many conduction electrons (or valence electrons) are in the sample?

When a photon enters the depletion zone of a p-njunction, the photon can scatter from the valence electrons there, transferring part of its energy to each electron, which then jumps to the conduction band. Thus, the photon creates electron–hole pairs. For this reason, the junctions are often used as light detectors, especially in the x-ray and gamma-ray regions of the electromagnetic spectrum. Suppose a single 662keV gamma-ray photon transfers its energy to electrons in multiple scattering events inside a semiconductor with an energy gap of 1.1eV, until all the energy is transferred. Assuming that each electron jumps the gap from the top of the valence band to the bottom of the conduction band, find the number of electron – hole pairs created by the process.
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