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Question

Number of particles is given by n equals negative D fraction numerator n subscript 2 end subscript minus n subscript 1 end subscript over denominator x subscript 2 end subscript minus x subscript 1 end subscript end fraction crossing a unit area perpendicular to X-axis in unit time, where n subscript 1 end subscript and n subscript 2 end subscript are number of particles per unit volume for the value of x meant to x subscript 2 end subscript and x subscript 1 end subscript. Find dimensions of D called as diffusion constant

  1. M to the power of 0 end exponent L T to the power of 2 end exponent    
  2. M to the power of 0 end exponent L to the power of 2 end exponent T to the power of negative 4 end exponent    
  3. M to the power of 0 end exponent L T to the power of negative 3 end exponent    
  4. M to the power of 0 end exponent L to the power of 2 end exponent T to the power of negative 1 end exponent    

The correct answer is: M to the power of 0 end exponent L to the power of 2 end exponent T to the power of negative 1 end exponent


    [n] = Number of particles crossing a unit area in unit time = left square bracket L to the power of negative 2 end exponent T to the power of negative 1 end exponent right square bracket
    open square brackets n subscript 2 end subscript close square brackets equals open square brackets n subscript 1 end subscript close square brackets equalsnumber of particles per unit volume = [L–3]
    \ D equals fraction numerator left square bracket n right square bracket   open square brackets x subscript 2 end subscript minus x subscript 1 end subscript close square brackets over denominator open square brackets n subscript 2 end subscript minus n subscript 1 end subscript close square brackets end fraction equals fraction numerator open square brackets L to the power of negative 2 end exponent T to the power of negative 1 end exponent close square brackets cross times left square bracket L right square bracket over denominator left square bracket L to the power of negative 3 end exponent right square bracket end fraction=open square brackets L to the power of 2 end exponent T to the power of negative 1 end exponent close square brackets

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