The wave function W can be factored into the product of three independent functi

Question

The wave function W can be factored into the product of three independent functions w(e,p,r) r)o(P)R(r). The square of the so-called radial function, R*(r), gives the relative probability of finding the electron at a single point at distance r from the nucleus. That should be distinguished from the so-called radial probability distribution 4nr2R, which gives the total probability of finding the electron anywhere at distance r from the nucleus i.e. in a spherical shell at distance This probability is precisely zero at only (n I) finite values of r. If the graph below represents the radial probability distribution for an electron in a p-orbital, what is its principal quantum number (n)? Note that 4 r2R2 also Count the number of points at which the radial probability distribution equals zero (include r = 0 but NOT r-infinity) then add to this the value of the secondary quantum number U approachs zero asymptotically as r goes to infinity. However it is precisely 0 at r=0. AT2R2 Make a point of understanding the distinction between R2 (the radial component of the probability of finding the electron at a single point at distance r from the nucleus) and the so-called radial probability 42r? (the total probability of finding the electron at distance r). Consider and compare the graphs for the 1s orbital, Figures 12.16 and 12.17 in Zumdahl "Chemical Principles" 8th ed. See also,Figures 12.33 and 12.34 No

Explanation / Answer

since there are 3 nodes at which probability of finding electron density is zero.

radial node = 3

radial node =n-l-1, where n= principle quantum number, l= azimuthal quantum number

this curve is 5p orbital because radial node=5-1-1=3

so for n value in 5p orbital is = 5

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