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Calculate the mean free path and the col...

Calculate the mean free path and the collsion frequency of air molecules, if the number of molecules per `cm^(3) is 3 xx 10^(19)`, the diameter of the molecule is `2 xx 10^(-8) cm` and average molecule speed is `1 km s^(-1)`.

Text Solution

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To solve the problem of calculating the mean free path and the collision frequency of air molecules, we will follow these steps: ### Step 1: Convert Given Values - **Number of molecules per cm³**: \( n = 3 \times 10^{19} \, \text{molecules/cm}^3 \) - **Convert to m³**: \[ n = 3 \times 10^{19} \, \text{molecules/cm}^3 \times (10^2 \, \text{cm/m})^3 = 3 \times 10^{25} \, \text{molecules/m}^3 \] ...
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Knowledge Check

  • The number of molecules present in 1 cm^(3) of water is :-

    A
    `2.7xx10^(19)`
    B
    `3.3xx10^(22)`
    C
    `6.02xx10^(20)`
    D
    1000
  • The average speed of air molecules is 485 "ms"^(-1) . At STP the number density is 2.7xx10^(25)m^(-3) and diameter of the air molecule is 2xx10^(-10) m . The value of mean free path for the air molecule is

    A
    `2.5xx10^(-7)m`
    B
    `2.9xx10^(-7)m`
    C
    `3.5xx10^(-7)m`
    D
    `3.9xx10^(-7)m`
  • The expression for mean free path (lamda) of molecules is given by [where n is no of molecules per unit volume and d molecular diameter of the gas]

    A
    `(sqrt(2))/(pind^(2))`
    B
    `(1)/(pnd^(2))`
    C
    `(1)/(sqrt(2)pind^(2))`
    D
    `(1)/(sqrt(2)pind)`
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    Calculate themean free path of molecule of a gas having number density (number of molecules per cm^(3) ) 2xx10^(8) and the diameter of the molecule is 10^(-5) cm

    Calculate the ratio of the mean free path of the molecules of two gases if the ratio of the number density per cm^(3) of the gases is 5:3 and the ratio of the diameters of the molecules of the gases is 4:5

    Calculate mean free path length lamda for molecules of an ideal gas at STP. It is known that molecular diameter is 2 x× 10^(–10) m.

    Calculate the ratio of the mean free path of molecules of two gases ig the ratio of the numbers denusity per cm^(3) of the gases is 5:3 and the ratio of the diameters of the molecules of the gases is 4:5

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