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Matter Waves

Let v⃗⃗1⃗, ...

Question

Let $_{1}, V_{m s}$ and $V_{P}$ respectively denote the mean speed, the root-mean-square, and the most probable speed, of the molecules in an ideal monoatomic gas at absolute temperature $T$ . The mass of a molecule is $m$ .

No molecule can have speed greater than

V_{r m s}

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No molecule can have speed less than

\frac{V_{P}}{\sqrt{2}}

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V_{P} < \to V < V_{r m s}

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The average kinetic energy of molecules is

\frac{3}{4} m v_{P}^{2}

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Solution

The correct options are
C $V_{P} < \to V < V_{r m s}$
D The average kinetic energy of molecules is $\frac{3}{4} m v_{P}^{2}$
$V_{r m s} = \sqrt{\frac{3 R T}{M}}$ and
$\to V = \sqrt{\frac{8 R T}{π M}} = \sqrt{2.55 \frac{R T}{M}}$
$V_{P} = \sqrt{\frac{2 R T}{M}}$
Hence (C) and (D) are correct.

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Let $\to v, v_{r m s}$ and $v_{2}$ respectively denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of a molecule is m. Then

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Let →v1,Vms and VP respectively denote the mean speed, the root-mean-square, and the most probable speed, of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of a molecule is m.

The correct options are C VP<→V<Vrms D The average kinetic energy of molecules is 34mv2PVrms=√3RTM and→V=√8RTπM=√2.55RTMVP=√2RTMHence (C) and (D) are correct.

Let $_{1}, V_{m s}$ and $V_{P}$ respectively denote the mean speed, the root-mean-square, and the most probable speed, of the molecules in an ideal monoatomic gas at absolute temperature $T$ . The mass of a molecule is $m$ .

The correct options are
C $V_{P} < \to V < V_{r m s}$
D The average kinetic energy of molecules is $\frac{3}{4} m v_{P}^{2}$
$V_{r m s} = \sqrt{\frac{3 R T}{M}}$ and
$\to V = \sqrt{\frac{8 R T}{π M}} = \sqrt{2.55 \frac{R T}{M}}$
$V_{P} = \sqrt{\frac{2 R T}{M}}$
Hence (C) and (D) are correct.