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Chapter 9: Problem 1276

The speeds of 5 molecules of a gas (in arbitrary units) are as follows: \(2,3,4,5,6\), The root mean square speed for these molecules is (A) \(4.24\) (B) \(2.91\) (C) \(4.0\) (D) \(3.52\)

Short Answer

Expert verified
The root mean square speed for these molecules is (A) \(4.24\).

Step by step solution

01

Square each speed

First, we find the square of each speed given in the problem. These are: \(2^2 = 4\), \(3^2 = 9\), \(4^2 = 16\), \(5^2 = 25\), and \(6^2= 36\).
02

Find the mean of the squared speeds

Now, we will find the mean of the squared speeds: \[(4 + 9 + 16 + 25 + 36) \div 5\] \[= \frac{90}{5}\] \[= 18\]
03

Find the square root of the mean

Finally, we will find the square root of the mean we calculated in step 2: \[\sqrt{18} \approx 4.24\]
04

Compare the calculated value with the options

Now, we will compare our calculated value with the given options: (A) \(4.24\) (B) \(2.91\) (C) \(4.0\) (D) \(3.52\) Our calculated value \(\approx 4.24\), which matches option (A), so the correct answer is (A) \(4.24\).

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Most popular questions from this chapter

The ratio of the vapor densities of two gases at a given temperature is $9: 8$, The ratio of the rms velocities of their molecule is (A) \(3: 2 \sqrt{2}\) (B) \(2 \sqrt{2}: 3\) (C) \(9: 8\) (D) \(8: 9\)

The temperature of a gas at pressure \(\mathrm{P}\) and volume \(\mathrm{V}\) is \(27^{\circ} \mathrm{C}\) Keeping its volume constant if its temperature is raised to \(927^{\circ} \mathrm{C}\), then its pressure will be (A) \(3 \mathrm{P}\) (B) \(2 \mathrm{P}\) (C) \(4 \mathrm{P}\) (D) \(6 \mathrm{P}\)

1 mole of gas occupies a volume of \(100 \mathrm{~m} 1\) at \(50 \mathrm{~mm}\) pressure. What is the volume occupied by two moles of gas at $100 \mathrm{~mm}$ pressure and at same temperature (A) \(50 \mathrm{ml}\) (B) \(200 \mathrm{ml}\) (C) \(100 \mathrm{ml}\) (D) \(500 \mathrm{~m} 1\)

The degrees of freedom for triatomic gas \(1 \mathrm{~s}\) (At room temperature) (A) 8 (B) 6 (C) 4 (D) 2

The root mean square velocity of a gas molecule of mass \(\mathrm{m}\) at a given temperature is proportional to (A) \(\mathrm{m}^{0}\) (B) \(\mathrm{m}^{-1 / 2}\) (C) \(\mathrm{m}^{1 / 2}\) (D) \(\mathrm{m}\)
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