For hydrogen 1s, R ( r ) = 2 ( 1/ a 0 ) 3/2 e − r / a 0 , a 0 = 0.529 Å. The ratio of radial probability densities at r=a₀ and at the nucleus is x e − y . Find x+y.

Question

For hydrogen 1s, R ( r ) = 2 ( 1/ a 0 ​ ) 3/2 e − r / a 0 ​ , a 0 ​ = 0.529 Å. The ratio of radial probability densities at r=a₀ and at the nucleus is x e − y . Find x+y.

TestHub · Accepted Answer

Given R, |R(r)|²=(4/a₀³)e^(-2r/a₀). Ratio at r=a₀ and zero is e⁻²=1×e⁻², so x=1,y=2,x+y=3. The source uses 'radial probability density' for |R|², not the shell-weighted r²|R|² distribution; the latter vanishes at the nucleus and would make the asked ratio undefined. Convention stated explicitly.

Chemistry - Atomic Structure Question with Solution | TestHub

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