Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
6-30. Show that the total probability density of the 2p orbitals is spherically symmetric by evaluating EV- (Use the wave functions in Table 6.6.)

6-30. Show that the total probability density of the 2p orbitals is spherically symmetric by evaluating EV- (Use the wave functions in Table 6.6.)

icon
Related questions
Question

This is a textbook question with the answer and table. Please show how the answer was derived.

6–30. Show that the total probability density of the 2p orbitals is spherically symmetric by evaluating Valm: (Use the wave functions in Table 6.6.) 1 o'e" (cos? 0 + sin² 0 cos² ø + sin² 0 sin² ø) 32л m=-1 z'o?e- [cos? e + sin? e (cos² + sin? ø)] 327a; %3D Z'o?e (cos² 0 + sin² e) 32n a, Z'o’e 32n a The sum depends only on the variable r (through ơ), so the total probability density of the 2p orbitals is spherically symmetric. 6–6. Use Equation 6.26 to generate the associated Legendre functions in Table 6.2. Pm' (x) = (1 – x?) m/2 _ dx dm P,(x) (6.26) P°(x) = (1 – x²)° oP dro Po(x) = P,(x) = 1 P°(x) = (1 – x²)° dxº d° oP,(x) = P,(x) = x P' (x) = (1 – x²)\/2 d dx - P,(x) = (1 – x²)/2 Pº(x) = (1 – x²)°- Jo P;(x) = P,(x) = P} (x) = (1 – x²)'2 P,(x) = 3x(1 – x?)!/2 dx d? P?(x) = (1 – x³) P,(x) = 3(1 – x²) d° P°(x) = (1 – x*)°P,(x) = P,(x) = dxº - 3x) O Type here to search 3:14 PM 危 x 10/3/2020
Transcribed Image Text:6–30. Show that the total probability density of the 2p orbitals is spherically symmetric by evaluating Valm: (Use the wave functions in Table 6.6.) 1 o'e" (cos? 0 + sin² 0 cos² ø + sin² 0 sin² ø) 32л m=-1 z'o?e- [cos? e + sin? e (cos² + sin? ø)] 327a; %3D Z'o?e (cos² 0 + sin² e) 32n a, Z'o’e 32n a The sum depends only on the variable r (through ơ), so the total probability density of the 2p orbitals is spherically symmetric. 6–6. Use Equation 6.26 to generate the associated Legendre functions in Table 6.2. Pm' (x) = (1 – x?) m/2 _ dx dm P,(x) (6.26) P°(x) = (1 – x²)° oP dro Po(x) = P,(x) = 1 P°(x) = (1 – x²)° dxº d° oP,(x) = P,(x) = x P' (x) = (1 – x²)\/2 d dx - P,(x) = (1 – x²)/2 Pº(x) = (1 – x²)°- Jo P;(x) = P,(x) = P} (x) = (1 – x²)'2 P,(x) = 3x(1 – x?)!/2 dx d? P?(x) = (1 – x³) P,(x) = 3(1 – x²) d° P°(x) = (1 – x*)°P,(x) = P,(x) = dxº - 3x) O Type here to search 3:14 PM 危 x 10/3/2020
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer