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Question

The figure shows a graph between ln invisible function application open vertical bar fraction numerator A subscript n end subscript over denominator A subscript 1 end subscript end fraction close vertical bar and ln|n|, where A subscript n end subscript is the area enclosed by the nth orbit in a hydrogen like atom. The correct curve is

  1. 4    
  2. 3    
  3. 2    
  4. 1    

The correct answer is: 4


    A subscript n end subscript equals pi r subscript n end subscript superscript 2 end superscriptÞ fraction numerator A subscript n end subscript over denominator A subscript 1 end subscript end fraction equals open parentheses fraction numerator r subscript n end subscript over denominator r subscript 1 end subscript end fraction close parentheses to the power of 2 end exponent equals open parentheses fraction numerator n over denominator 1 end fraction close parentheses to the power of 4 end exponent.left parenthesis because r subscript n end subscript proportional to n to the power of 2 end exponent right parenthesis
    Taking loge both the side log subscript e end subscript invisible function application fraction numerator A subscript n end subscript over denominator A subscript 1 end subscript end fraction equals 4 log subscript e end subscript invisible function application left parenthesis n right parenthesis
    Comparing it with y = mx + c, graph (4) is correct

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