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Cationic Radius

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Question

Calculate ratio of the radius of 2nd orbit of H atom and 3rd?

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Solution

$B o h r r a d i u s = \frac{n^{2} a_{0}}{Z} W h e r e n - n u m b e r o f o r b i t Z - a t o m i c n u m b e r a_{0} - B o h r r a d i u s = 0.0529 n m F o r 2 n d o r b i t o f h y d r o g e n n = 2 a n d Z = 1 B o h r r a d i u s = \frac{2^{2} a_{0}}{1} = 4 a_{0} F o r 3 r d o r b i t o f h y d r o g e n n = 3 a n d Z = 1 B o h r r a d i u s = \frac{3^{2} a_{0}}{1} = 9 a_{0} S o t h e r a t i o o f B o h r o r b i t o f 2 n d t o 3 r d i s = 4 a_{0} : 9 a_{0} = 4 : 9$ $B o h r r a d i u s = \frac{n^{2} a_{0}}{Z} W h e r e n - n u m b e r o f o r b i t Z - a t o m i c n u m b e r a_{0} - B o h r r a d i u s = 0.0529 n m F o r 2 n d o r b i t o f h y d r o g e n n = 2 a n d Z = 1 B o h r r a d i u s = \frac{2^{2} a_{0}}{1} = 4 a_{0} F o r 3 r d o r b i t o f h y d r o g e n n = 3 a n d Z = 1 B o h r r a d i u s = \frac{3^{2} a_{0}}{1} = 9 a_{0} S o t h e r a t i o o f B o h r o r b i t o f 2 n d t o 3 r d i s = 4 a_{0} : 9 a_{0} = 4 : 9$

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