Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

At the center of the Sun, the density of the gas is $1.5 \times 10^{5} kg / m^{3}$ and the composition is essentially 35% hydrogen by mass and 65% helium by mass. (a) What is the number density of protons there? (b) What is the ratio of that proton density to the density of particles in an ideal gas at standard temperature (0°C) and pressure $(1.01 \times 10^{5} Pa)$ ?

a) The number of density of protons is $3.1 \times 10^{31} protons / m^{3}$ .

b) The required ratio is $1.2 \times 10^{6}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Describe the expression to calculate the number density of protons

At the center of the Sun the density of the hydrogen is 35% from the gas density,

$ρ_{H} = 0.35 ρ$

The gas density is the number density of H multiplied by the mass of H.

$ρ_{H} = n_{H} m_{H}$

Combine above two equations.

$n_{H} m_{H} = 0.35 ρ n_{H} = \frac{0.35 ρ}{m_{H}} . . . . . . . . . . (1)$

Here, $ρ$ is density, and $m_{H}$ is mass of hydrogen atom.

Step 2(a): Find the number density of protons

Substitute all the known values in equation (1).

$n_{H} = \frac{0.35 (1.5 \times 10^{5} k g / m^{3})}{1.67 \times 10^{- 27} k g} = 3.1 \times 10^{31} p r o t o n s / m^{3}$

Therefore, the number of density of protons is $3.1 \times 10^{31} p r o t o n s / m^{3}$ .

Step 3(b): Find the ratio of proton density to the density of particles

From the ideal gas law,

$P V = N k T \frac{N}{V} = \frac{P}{k T} . . . . . . . . . . . (2)$

Substitute all the known values in equation (2).

$\frac{N}{V} = \frac{1.01 \times 10^{5} P a}{(1.38 \times 10^{- 23} J / K) (273 K)} = 2.68 \times 10^{25} p r o t o n s / m^{3}$

Find the ratio of proton density to the density of particles as follows.

$\frac{n_{H}}{N / V} = \frac{3.1 \times 10^{31} p r o t o n s / m^{3}}{2.68 \times 10^{25} p r o t o n s / m^{3}} = 1.2 \times 10^{6}$

Therefore, the required ratio is $1.2 \times 10^{6}$ .

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Describe the expression to calculate the number density of protons

Step 2(a): Find the number density of protons

Step 3(b): Find the ratio of proton density to the density of particles

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Describe the expression to calculate the number density of protons

Step 2(a): Find the number density of protons

Step 3(b): Find the ratio of proton density to the density of particles

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