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The dimension of the quantity 1/epsilon0...

The dimension of the quantity `1/epsilon_0 e^2/(hc)` is (e charge of electron,h Planck's constant and c=velocity of light)

A

`[M^(-1) L^(-3) T^2 A]`

B

`[M^(0) L^(0) T^0 A^0]`

C

`[ML^(3) T^(-4) A^(-2)]`

D

`[M^(-1) L^(-3) T^4 A^2]`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The dimensions of the quantity hc (where h=h/(2pi) ) is

    A
    `[ML^(2)T^(-1)]`
    B
    `[MLT^(-1)]`
    C
    `[ML^(3)T^(-2)]`
    D
    `[ML^(3)T^(-1)]`
  • The dimensions of the quantity namely (mu_(0)ce^(2))/(2h) where mu_(0) permeability of free space, c - velocity of light, e - electronic charge and h = (h)/(2pi) being Planck's constant

    A
    `[M^(0)LT]`
    B
    `[M^(0)L^(0)T]`
    C
    `[M^(0)L^(0)T^(0)]`
    D
    `[M^(-2)L^(-1)T^(-3)]`
  • The de-Broglie wavelength of an electron is same as the wavelength of a photon. The energy of a photon is ‘x’ times the K.E. of the electron, then ‘x’ is: (m-mass of electron, h-Planck’s constant, c - velocity of light)

    A
    `(hc)/(2lambdam)`
    B
    `(2lambdamc)/(h)`
    C
    `(2lambdac)/(hm)`
    D
    `(2lambdam)(ch)`
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    State whether the following statement is true or false. Give very brief reason in support of your answer. The quantity e^(2)/(2 epsi_(0) hc) is dimensionless. Here e, h and c are electronic charge, Planck's constant and velocity of light respectively and epsi_(0) is the permittivity constant of free space.

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