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Question
Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (An/A1) against ln(n)
(a) will pass through the origin
(b) will be a straight line with slope 4
(c) will be a monotonically increasing nonlinear curve
(d) will be a circle
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Solution
(a) will pass through the origin
(b) will be a straight line with slope 4
The radius of the nth orbit of a hydrogen atom is given by
`r_n = n^2a_0`
Area of the nth orbit is given by
`A_n = pir_n^2 = pin^4a_0^2`
`A_1 = pia_0^2`
`rArr In ((An)/(A_1)) = ln ((pin^4a_0^2)/(pia_0^2))`
In `((An)/A_1) = 4 ln n.........(1)`
From the above expression, the graph of ln (An/A1) against ln(n) will be a straight line passing through the origin and having slope 4.
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