Chapter 19: Q18P (page 578)

Question: The temperature and pressure in the Sun’s atmosphere are $2.00 \times 10^{6} K$ and 0.0300 paCalculate the rms speed of free electrons (mass $9.11 \times 10^{- 31} kg$ ) there, assuming they are an ideal gas.

Short Answer

Expert verified

Answer

The rms speed of free electrons is $9.53 \times 10^{6} \frac{m}{s}$ .

Step by step solution

Given

$T = 2.00 \times 10^{6} K, p = 0.0300 Pa, m = 9.11 \times 10^{- 31} kg$

Determine the concept

Find the RMS speed using the formula for root-mean-square speed. MS speed is defined as the square root of the mean of the square of speeds of all molecules.

Formula is as follow:

$v = \sqrt{\frac{3 R T}{M}}$

Here, M is mass, Tis temperature, v is velocity and R is universal gas constant.

Determine the rms speed of free electrons

The rms speed of electrons is,

$v = \sqrt{\frac{3 R T}{M}} M = m N_{A} a n d R = k N_{A} v = \sqrt{\frac{3 k N_{A} T}{m N_{A}}} ∴ v = \sqrt{\frac{3 k T}{m}}$

Substitute the values and solve as:

$∴ v = \sqrt{\frac{3 (1.38 \times 10^{- 23}) 2.00 \times 10^{6}}{9.11 \times 10^{- 31}}} v = 9.533 \times 10^{6} v = 9.53 \times 10^{6} \frac{m}{s}$

Hence, the rms speed of free electrons is $v = 9.53 \times 10^{6} \frac{m}{s}$ .

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Question: The temperature and pressure in the Sun’s atmosphere are $2.00 \times 10^{6} K$ and 0.0300 paCalculate the rms speed of free electrons (mass $9.11 \times 10^{- 31} kg$ ) there, assuming they are an ideal gas.

Short Answer

Step by step solution

Given

Determine the concept

Determine the rms speed of free electrons

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Question: The temperature and pressure in the Sun’s atmosphere are 2.00×106Kand 0.0300 paCalculate the rms speed of free electrons (mass 9.11×10-31kg) there, assuming they are an ideal gas.

Short Answer

Step by step solution

Given

Determine the concept

Determine the rms speed of free electrons

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Measurements

Mechanics and Materials

Classical Mechanics

Geometrical and Physical Optics

Radiation

Study anywhere. Anytime. Across all devices.

Question: The temperature and pressure in the Sun’s atmosphere are $2.00 \times 10^{6} K$ and 0.0300 paCalculate the rms speed of free electrons (mass $9.11 \times 10^{- 31} kg$ ) there, assuming they are an ideal gas.