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Physics-

General

Easy

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

4
3
2
1

The correct answer is: 4

$A subscript n end subscript equals pi r subscript n end subscript superscript 2 end superscript rightwards double arrow$ $fraction numerator A subscript n end subscript over denominator A subscript 1 end subscript end fraction equals open parentheses fraction numerator r subscript n end subscript over denominator r subscript 1 end subscript end fraction close parentheses to the power of 2 end exponent equals open parentheses fraction numerator n over denominator 1 end fraction close parentheses to the power of 4 end exponent blank left parenthesis because r subscript n end subscript proportional to n to the power of 2 end exponent right parenthesis$
Taking log_e 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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