Q51P The saturation magnetization Mm... [FREE SOLUTION]

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Chapter 32: Q51P (page 970)

The saturation magnetization $M_{\max}$ of the ferromagnetic metal nickel is $4.70 脳 10^{5} A / m$ . Calculate the magnetic dipole moment of a single nickel atom. (The density of nickel is $8.90 g / {cm}^{3}$ , and its molar mass is $58.71 g / mol$ .)

Short Answer

Expert verified

Magnetic dipole moment of a single nickel atom is, $渭_{B} = 5.15 脳 10^{- 24} A m^{2}$ .

Step by step solution

Listing the given quantities

Saturation magnetization $M_{\max} = 4.70 脳 10^{5} A / m$

Density of nickel is $蚁 = 8.90 g / {cm}^{3}$

Molar mass of nickel is $58.71 g / mole$

Understanding the concepts of magnetic dipole moment

We use the concept of magnetic dipole moment. Using the equations, we findthenumber of atoms per unit volume, and then we can findthemagnetic dipole moment.

Formulae:

$渭_{B} = \frac{M_{\max}}{n}$

$n = \frac{{蚁N}_{A}}{M}$

Calculations of the magnetic dipole moment of a single nickel atom

We find the number of atoms per unit volume.

Using equation

$\begin{matrix} n = \frac{{蚁N}_{A}}{M} \\ = \frac{(8.90) (6.023 脳 10^{23})}{58.71} \\ = 9.126 脳 10^{22} \frac{atoms}{{cm}^{3}} \end{matrix}$

We can convert it in $atoms / m^{3}$ .We can write

$\begin{matrix} n = 9.126 脳 10^{22} \frac{atoms}{{cm}^{3}} 脳 {(\frac{1 cm}{10^{- 2} m})}^{3} \\ = 9.126 脳 10^{22} \frac{atoms}{{cm}^{3}} 脳 1 \frac{{cm}^{3}}{10^{- 6} m^{3}} \\ = 9.126 脳 10^{28} \frac{atoms}{m^{3}} \end{matrix}$

Substituting this value in magnetic dipole moment,

$\begin{matrix} 渭_{B} = \frac{M_{\max}}{n} \\ = \frac{4.70 脳 10^{5}}{9.126 脳 10^{28}} \\ = 5.15 脳 10^{- 24} A m^{2} \end{matrix}$

Magnetic dipole moment of a single nickel atom is, $渭_{B} = 5.15 脳 10^{- 24} A m^{2}$ .

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91影视

The saturation magnetization $M_{\max}$ of the ferromagnetic metal nickel is $4.70 脳 10^{5} A / m$ . Calculate the magnetic dipole moment of a single nickel atom. (The density of nickel is $8.90 g / {cm}^{3}$ , and its molar mass is $58.71 g / mol$ .)

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of magnetic dipole moment

Calculations of the magnetic dipole moment of a single nickel atom

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

The saturation magnetization Mmax of the ferromagnetic metal nickel is4.70脳105A/m . Calculate the magnetic dipole moment of a single nickel atom. (The density of nickel is8.90g/cm3, and its molar mass is58.71g/mol .)

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of magnetic dipole moment

Calculations of the magnetic dipole moment of a single nickel atom

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Electrostatics

Magnetism

Radiation

Force

Astrophysics

Study anywhere. Anytime. Across all devices.

The saturation magnetization $M_{\max}$ of the ferromagnetic metal nickel is $4.70 脳 10^{5} A / m$ . Calculate the magnetic dipole moment of a single nickel atom. (The density of nickel is $8.90 g / {cm}^{3}$ , and its molar mass is $58.71 g / mol$ .)