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What are the units of K = 1/(4 pi epsilo...

What are the units of `K = 1/(4 pi epsilon_0)`?

A

`C^2N^(-2)m^(-2)`

B

`Nm^2C^(-2)`

C

`Nm^2C^2`

D

Unitless.

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Knowledge Check

  • What are the units.of K=1/(4pivarepsilon_(0))

    A
    `C^(2)N^(-1)m^(-2)`
    B
    `Nm^(2)C^(-2)`
    C
    `Nm^(2)C^(2)`
    D
    Unitless

  • What are the units of k for the rate law : Rate = k [A][B]^2 , when the concentration unit is mol/L ?

    A
    `s^(-1)`
    B
    `s`
    C
    `L mol^(-1) s^(-1)`
    D
    `L^2 mol^(-2)s^(-1)`

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    What is unit of 1 // mu_0 epsilon_0 ?

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    What is the SI unit of epsilon_0 ?

    There is another useful system of units, besides the SI/MKS. A system, called the cgs system. In this system Coulumb's law is given by vecF = (Qq)/(r^2) hatr where the distance r is measured in cm (=10^(-2) m) , F in dynes (= 10^(-5) N) and the charges in electrostatic units (es units), where 1es unit of charge = 1/[3] xx 10^(-9) C . The number [3] actually arises the speed of light in vacuum which now taken to be exactly given by c = 2.99792458 xx 10^8 m/s . An approximate value of c then is c = [3] xx 10^8 m/s . Write 1 esu of charge = x C, where x is a dimensoinless number. Show that this gives 1/(4pi epsilon_0) = (10^(-9)/x^2)(N.m^2)/(C^2) with x = 1/[3] xx 10^(-9) , we have 1/(4pi epsilon_0)= [3]^2 xx 10^9 (Nm^2)/(C^2) or 1/(4pi epsilon_0)= (2.99792458)^2 xx 10^9 (Nm)^2/(C)^2 (exactly).

    What is the unit of K_(p) for the reaction ? CS_(2)(g)+4H_(4)(g)hArrCH_(4)(g)+2H_(2)S(g)

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