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Question: A gas at 300 K has pressure 4 × 10–10 N m–2. If *k*B = 1.38 × 10–23 J K–1, the number of molecules p...

A gas at 300 K has pressure 4 × 10–10 N m–2. If kB = 1.38 × 10–23 J K–1, the number of molecules per cm3 of the order of

A

103

B

105

C

106

D

109

Answer

105

Explanation

Solution

Using, PV = nRT = nN (RN)T=nNkBT\left( \frac{R}{N} \right)T = nNk_{B}T

nNV=PkB=\frac{nN}{V} = \frac{P}{k_{B}} =number of molecules

∴\thereforeNumber of molecules/cm3=PkBT×10−6cm^{3} = \frac{P}{k_{B}T} \times 10^{- 6}

=4×10−10×10−61.38×10−23×300=105= \frac{4 \times 10^{- 10} \times 10^{- 6}}{1.38 \times 10^{- 23} \times 300} = 10^{5}