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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 $ln invisible function application vertical line n vertical line$ , where $A subscript n end subscript$ is the area enclosed by the $n$ th orbit in a hydrogen like atom. The correct curve is $ln invisible function application open vertical bar A subscript n over A subscript 1 close vertical bar$

4
3
2
1

The correct answer is: 4

$A subscript n end subscript equals pi r subscript n end subscript superscript 2 end superscript rightwards double arrow fraction numerator A subscript n end subscript over denominator A subscript 1 end subscript end fraction equals open parentheses fraction numerator r subscript n end subscript over denominator r subscript 1 end subscript end fraction close parentheses to the power of 2 end exponent equals open parentheses fraction numerator n over denominator 1 end fraction close parentheses to the power of 4 end exponent blank left square bracket because r subscript n end subscript proportional to n to the power of 2 end exponent right square bracket$
Taking $l o g subscript e end subscript$ on both the sides $log subscript e end subscript invisible function application fraction numerator A subscript n end subscript over denominator A subscript 1 end subscript end fraction equals 4 log subscript e end subscript invisible function application left parenthesis n right parenthesis$
Comparing it with $y equals m x plus c$ , graph (4) is correct

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