Q.

Let An be the area enclosed by the nth orbit in a hydrogen atom.  The graph of ln(An/A1) against ln(n): (Here A1 is the first orbit.)

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a

will pass through origin

b

will be straight line with slope = 4

c

will be a monotonically increasing non-linear curve

d

it will be a circle

answer is A.

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Detailed Solution

It cant be a circle, since the orbits are in elliptical shape as described by sommerfield. The mathematical reason is we get the equationy=2(logn2)x, if x=0 the line passes throgh the origin. The equation is y=mx+C form.
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Let An be the area enclosed by the nth orbit in a hydrogen atom.  The graph of ln(An/A1) against ln(n): (Here A1 is the first orbit.)