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Chapter 20: 27 P (page 805)

Calculate the mobile electron density for nickel. A mole of nickel has a mass of 59g (0.059kg), and one mobile electron is released by each atom in metallic nickel. The density of nickel is about 8.8g/cm3, or8.8×103kg/m3

Short Answer

Expert verified

The mobile electron density is, 8.98×1028kg/m3.

Step by step solution

01

Identification of the given data 

The given data can be listed below as,

· The mass of one mole of nickel is, 59g or 0.059 kg.

· The density of nickel is, ρ=8.8g/cm3orrole="math" localid="1668551564749" ρ=8.8×103kg/m3

02

Significance of the Avogadro’s number

The quantity of particles in one mole of a substance is known as Avogadro's number. It can be used to change moles into particles or particles into particles.

03

Determination of the mobile electron density for nickel

According to the question,

1 mole of nickel = Avogadro atoms = 0.059kg

1m3of nickel = ρkg

ρkg=ρ0.059moles=Avogadro×ρ0.059atoms

The mobile electron density is expressed as,

=ρ0.059moles=Avagadro×ρ0.059atoms

Substitute all the value in the above equation

The mobile electron density is,

=6.023×1023×8.8×103kg/m30.059=8.98×1028kg/m3

Hence the mobile electron density is,8.98×1028kg/m3

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Most popular questions from this chapter

We will consider the possibility that a free electron acted on by an electric field could gain enough energy to ionize an air molecule in a collision. (a) Consider an electron that starts from rest in a region where there is an electric field (due to some charged objects nearby) whose magnitude is nearly constant. If the electron travels a distance dand the magnitude of the electric field is E ,what isthe potential difference through which the electron travels? (Pay attention to signs: Is the electron traveling with the electric field or opposite to the electric field?) (b) What is the change in potential energy of the system in this process? (c) What is the change in the kinetic energy of the electron in this process? (d) We found the mean free path of an electron in air to be about role="math" localid="1662205184726" 5×10-7 m, and in the previous question you calculated the energy required to knock an electron out of an atom. What is the magnitude of the electric field that would be required in order for an electron to gain sufficient kinetic energy to ionize a nitrogen molecule? (e) The electric field required to cause a spark in air is observed to be about 3×106 V/mat STP. What is the ratio of the magnitude of the field you calculated in the previous part to the observed value at STP? (f) What is it reasonable to conclude about this model of how air becomes ionized? (1) Since we used accurate numbers, this is a huge discrepancy, and the model is wrong. (2) Considering the approximations we made, this is pretty good agreement, and the model may be correct.

A bar magnet whose magnetic dipole moment is 15 A.m2is aligned with an applied magnetic field of 4 T. How much work must you do to rotate the bar magnet 180°to point in the direction opposite to the magnetic field?

We will consider the possibility that a free electron actedon by an electric field could gain enough energy to ionize anair molecule in a collision. (a) Consider an electron that startsfrom rest in a region where there is an electric field (due to somecharged objects nearby) whose magnitude is nearly constant. Ifthe electron travels a distance dand the magnitude of the electric field is E,what isthe potential difference through which the electron travels? (Pay attention to signs: Is the electron traveling with the electric field or opposite to the electric field?) (b) What is the change in potential energy of the system in this process? (c) What is the change in the kinetic energy of the electron in this process? (d) We found the mean free path of an electron in air to be about 5×10-7 m, and in the previous question you calculated the energy required to knock an electron out of an atom. What is the magnitude of the electric field that would be required in order for an electron to gain sufficient kinetic energy to ionize a nitrogen molecule? (e) The electric field required to cause a spark in air is observed to be about 3×106 V/m at STP. What is the ratio of the magnitude of the field you calculated in the previous part to the observed value at STP? (f) What is it reasonable to conclude about this model of how air becomes ionized? (1) Since we used accurate numbers, this is a huge discrepancy, and the model is wrong. (2) Considering the approximations we made, this is pretty good agreement, and the model may be correct.

You hold your magnet perpendicular to a bar of copper that is connected to a battery (Figure 20.84). Describe the directions of the components of the electric field at the center of the copper bar, both parallel to the bar and perpendicular to the bar. Explain carefully.

:In Figure 20.121 a bar 11 cm long with a rectangular cross section 3 cm high and 2 cm deep is connected to a 1.2 V battery and an ammeter. The resistance of the copper connecting wires and the ammeter, and the internal resistance of the battery, are all negligible compared to the resistance of the bar.

Using large coils not shown on the diagram, a uniform magnetic field of 1.8 T was applied perpendicular to the bar (out of the page, as shown). A voltmeter was connected across the bar, with the connections across the bar carefully placed directly across from each other.

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