Ψ 1 s = π 1 ( a 0 1 ) 3/2 e − a 0 r (for H-atom) The ratio of probability density at the nucleus (r = 0) to the probability density (r = a 0 ) is e x . Find x.

Question

Ψ 1 s ​ = π ​ 1 ​ ( a 0 ​ 1 ​ ) 3/2 e − a 0 ​ r ​ (for H-atom) The ratio of probability density at the nucleus (r = 0) to the probability density (r = a 0 ) is e x . Find x.

TestHub · Accepted Answer

Probability density = ψ 2 ψ 2 a t ( r = a 0 ​ ) = [ π ​ 1 ​ ( a 0 ​ 1 ​ ) 3/2 e − a 0 ​ a 0 ​ ​ ] 2 ψ 2 a t ( r = 0 ) = [ π ​ 1 ​ ( a 0 ​ 1 ​ ) 3/2 e − a 0 ​ 0 ​ ] 2 ψ 2 ( r = a 0 ​ ) ψ 2 ( r = 0 ) ​ = e + 2

Chemistry - Atomic Structure Question with Solution | TestHub

Doubts & Discussion