For the 1s orbital of the Hydrogen atom, the radial wave function is given as: R ( r ) = 1 π ( 1 a O ) 3 2 e − r a O (Where a O = 0.529 ∘A)The ratio of radial probability density of finding an electron at r = a O to the radial probability density of finding an electron at the nucleus is given as ( x . e − y ). Calculate the value of (x+y).

Question

For the 1s orbital of the Hydrogen atom, the radial wave function is given as:   R  (  r  )  =      1          π        (      1          a      O            )                  3        2                  e                            −          r                          a          O                     (Where       a    O    =  0.529 ∘A)The ratio of radial probability density of finding an electron at   r  =      a    O   to the radial probability density of finding an electron at the nucleus is given as (  x  .      e          −      y      ). Calculate the value of (x+y).

Sterling Cameron · Accepted Answer

Radial probability density at r    Radial probability ensity at r    =                    R        2            (              a        O            )                      R        2            (      O      )      For 1s orbital:       R          (      r      )        =      1          π        (      1          a      O            )                  3        2                  e                            −          t                          a          O                    Therefore,                    R        2            (              a        O            )                      R        2            (      O      )        =            (              1                  π                      a            O            3                              )              e                                            −              2              r                                      a              O                                                  (              1                  π                      a            O            3                              )              e        O              =      e          −      2      Thus, according to x.       e          −      y       given in question.Here, x=1, y=2 and (X+Y)=3

For the 1s orbital of the Hydrogen atom, the radial wave function is given as: R(r)=1/(sqrt pi)

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