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The work done by a gas molecule in an isolated system is given by W = α β 2 e − x 2 α k T , where x is the displacement, k is the Boltzmann constant and T is the temperature. a and b are constants. Then the dimensions of b will be:

Option 1 -

[ M L T − 2 ]

Option 2 -

[ M L 2 T − 2 ]

Option 3 -

[ M 2 L T 2 ]

Option 4 -

[ M 0 L T 0 ]

0 2 Views | Posted 3 weeks ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 weeks ago
    Correct Option - 1


    Detailed Solution:

    Since, x 2 α k T should be dimensionless.

    So, dimension of  α , [ α ] = L 2 M L 2 T − 2 = M − 1 T 2

    Dimension of  α β 2 should be that of W.

    So, [ α β 2 ] = M L 2 T − 2

    ⇒ [ β 2 ] = M L 2 T − 2 M − 1 T 2 = M 2 L 2 T − 4 ⇒ [ β ] = M L T − 2

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