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Chapter 12: Q19Q (page 508)

A carbon nanoparticle (very small particle) contains 6000 carbon atoms. According to the Einstein model of a solid, how many oscillators are in this block?

Short Answer

Expert verified

The number of oscillators in the block is $18000$

Step by step solution

01

Identification of the given data

The given data can be listed below as,

The number of carbon atoms is, $N = 6000$

02

Determination the number of oscillators in a carbon nanoparticles block.

The relation of number of oscillators in the block is expressed as,

n = 3 (N)

Here $n$ represents the number of oscillators in the block

Substitute all the known values in the above relation.

$n = 3 \times 6000 = 18000$

Thus, the number of oscillators in the block is .

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Most popular questions from this chapter

A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are $4 \times 10^{- 21} J$ apart. (a) When the nanoparticle’s energy is in the range $5 \times 4 \times 10^{- 21} J$ J to, $6 \times 4 \times 10^{- 21} J$ what is the approximate temperature? (In order to keep precision for calculating the specific heat, give the result to the nearest tenth of a kelvin.) (b) When the nanoparticle’s energy is in the rangerole="math" localid="1657107429075" $8 \times 4 \times 10^{- 21} J$ to, $9 \times 4 \times 10^{- 21} J$ what is the approximate temperature? (In order to keep precision for calculating the specific heat, give the result to the nearest tenth of a degree.) (c) When the nanoparticle’s energy is in the range $5 \times 4 \times 10^{- 21} J$ to $9 \times 4 \times 10^{- 21} J$ , what is the approximate heat capacity per atom? Note that between parts (a) and (b) the average energy increased from 5.5 quanta to 8.5 quanta. As a check, compare your result with the high temperature limit of $3 k_{B}$ .

Approximately what fraction of the sea-level air density is found at the top of Mount Everest, a height of 8848 m above sea level?

A gas is made up of diatomic molecules. At temperature $T_{1}$ ,the ratio of the number of molecules in vibrational energy state 2to the number of molecules in the ground state is measured, andfound to be 0.35. The difference in energy between state 2 andthe ground state is ΔE. (a) Which of the following conclusions is

correct? (1) $∆ E \approx k_{B} T_{1}$ , (2) $∆ E ≪ k_{B} T_{1}$ , (3) $∆ E ≫ k_{B} T_{1}$

(b) At a different temperature $T_{2}$ , the ratio is found to be $8 \times 10^{- 5}$ . Which of the following is true? (1) $∆ E \approx k_{B} T_{2}$ , (2) $∆ E ≪ k_{B} T_{2}$ ,(3) $∆ E ≫ k_{B} T_{2}$ .

Suppose that you look once every second at a system with $300$ oscillators and $100$ energy quanta, to see whether your favorite oscillator happens to have all the energy (all $100$ quanta) at the instant you look. You expect that just once out ofrole="math" localid="1655710247969" $1.7 \times 10^{96}$ times you will find all of the energy concentrated on your favorite oscillator. On the average, about how many years will you have to wait? Compare this to the age of the Universe, which is thought to be aboutrole="math" localid="1655710262469" $1 \times 10^{10}$ years.role="math" localid="1655710345899" $1 Y \approx π \times 10^{7} S$

The entropy S of a certain object (not an Einstein solid) is the following function of the internal energy $E : S = {bE}^{1 / 2}$ , where b is a constant. (a) Determine the internal energy of this object as a function of the temperature.

(b) What is the specific heat of this object as a function of the temperature?

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