How to find a unit vector normal to the surface x 3 + y 3 + 3 x y z = 3 ay the point(1,2,-1)?

Question

How to find a unit vector normal to the surface             x      3        +          y      3        +    3    x    y    z    =    3   ay the point(1,2,-1)?

Roy Mcclain · Accepted Answer

The following is an expression for energy:      E    0    =            −      (      2.18      ×              10                  −          18                    )              Z        2                    n      2       Where, Z = atomic number of the atom n = principal quantum number For ionization from       n    1    =  5     t  o         n    2    =  ∞,  △  E  =      E          ∞        −      E    5      =  [                    −        (        2.18        ×                  10                      −            18                          J        )        (        1                  )          2                            (        ∞                  )          2                      −                    −        (        2.18        ×                  10                      −            18                          J        )        (        1                  )          2                            (        5                  )          2                      ]    =  (  2.18  ×      10          −      18        J  )  (  1  (  5      )    2    )    (  S  i  n  c  e         1    ∞    =  0  )    =  0.0872  ×      10          −      18        J    △  E  =  8.72  ×      10          −      20        J Therefore, the energy required for ionization from n = 5 to   n  =  ∞ Energy required for n1 = 1 to   n  =  ∞, is   8.72  ×      10          −      20        J.  △  E  =      E          ∞        −      E    1      =  [                    −        (        2.18        ×                  10                      −            18                          )        (        1                  )          2                            (        ∞        )              −                    −        (        2.18        ×                  10                      −            18                          )        (        1                  )          2                            (        1                  )          2                      ]    =  (  2.18  ×      10          −      18        )    =  2.18  ×      10          −      18        J Thus, less energy is required to ionize an electron in the 5th orbital of hydrogen atom as compared to that in the ground state.

How much energy is required to ionise a H atom if the electron occupies n = 5 orbit?

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