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The average mass of an air molecule is 4.8 × 10^-26 kg - AQA - A-Level Physics - Question 10 - 2018 - Paper 2

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The average mass of an air molecule is 4.8 × 10^-26 kg. What is the mean square speed of an air molecule at 750 K?

Worked Solution & Example Answer:The average mass of an air molecule is 4.8 × 10^-26 kg - AQA - A-Level Physics - Question 10 - 2018 - Paper 2

Step 1

Calculate the mean square speed using the formula

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Answer

The mean square speed of a gas molecule can be calculated using the formula:

v_{rms} = rac{3kT}{m}

Where:

  • vrmsv_{rms} is the root mean square speed,
  • kk is the Boltzmann constant (1.38×10−23extJ/K1.38 × 10^{-23} ext{ J/K}),
  • TT is the temperature in Kelvin,
  • mm is the mass of a molecule in kilograms.

For this problem:

  • T=750extKT = 750 ext{ K},
  • m=4.8×10−26extkgm = 4.8 × 10^{-26} ext{ kg}.

Plugging in the values, we calculate:

v_{rms} = rac{3 imes (1.38 × 10^{-23}) imes 750}{4.8 × 10^{-26}}

Step 2

Evaluate the expression

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Answer

Calculating the numerator:

3imes(1.38×10−23)imes750=3.105×10−203 imes (1.38 × 10^{-23}) imes 750 = 3.105 × 10^{-20}

Now, calculate the mean square speed:

v_{rms} = rac{3.105 × 10^{-20}}{4.8 × 10^{-26}} ≈ 6.46 × 10^5 ext{ m}^2/ ext{s}^2

This approximates to 6.5 × 10^5 m²/s², leading us to conclude the correct answer is C.

Step 3

Choose the correct answer option

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Answer

C. 6.5 × 10^5 m²/s²

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