Solve the following problem step by step (please solve quickly, I'll give 5 upvotes) Topic: Atomic Physics (a) Find the location in space where the electron is most likely to be found in a hydrogenid orbital 5/2 z exp (-)? (NOTE: atomic number is Z and Cartesian coordinate is z); Zr 2pz = 4/2n \aB 2ав. (b) calculate the expected value (2pz |r | 2pz) of the radial position of the electron in the 2pz orbital directly by calculating the integral and check the result with the equation : (r)ném = (ntm[r|n&m) = "" |1 +÷(1– n2

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Solve the following problem step by step (please solve quickly, l'll give 5 upvotes)
Topic: Atomic Physics
(a) Find the location in space where the electron is most likely to be found in a hydrogenid orbital
5/2
z exp (-)? (NOTE: atomic number is Z and Cartesian coordinate is z);
1
Zr
2pz
4/2n \aB.
2ав.
(b) calculate the expected value (2pz |r | 2pz) of the radial position of the electron in the 2pz orbital directly by
calculating the integral and check the result with the equation :
п?ав
[1+(1
e(l+1)
(r)nem = (n{m|r|n{m)
n2
Transcribed Image Text:Solve the following problem step by step (please solve quickly, l'll give 5 upvotes) Topic: Atomic Physics (a) Find the location in space where the electron is most likely to be found in a hydrogenid orbital 5/2 z exp (-)? (NOTE: atomic number is Z and Cartesian coordinate is z); 1 Zr 2pz 4/2n \aB. 2ав. (b) calculate the expected value (2pz |r | 2pz) of the radial position of the electron in the 2pz orbital directly by calculating the integral and check the result with the equation : п?ав [1+(1 e(l+1) (r)nem = (n{m|r|n{m) n2
Expert Solution
Step 1

(a)

Given:

The expression for a hydrogenid orbital is given as

2 pz=142π (ZaB)5/2z exp(-Zr2 aB)       =142π(ZaB)5/2(rcosθ)exp(-Zr2 aB)Since, in spherical polar coordinate system z=rcosθ

Calculation:

The most probable position is evaluated as follows

ddr(2 pz)=0ddr{142π (ZaB)5/2(rcosθ)exp(-Zr2 aB)=0cosθ e-Zr2 aB-Zr2 aBcosθ e-Zr2 aB=0(1-Zr2 aB)cosθ e-Zr2 aB=0(1-Zr2 aB)=01=Zr2 aBr=2 aBZHence the required position or location in space is (2 aBZ).

 

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