**Radial Wave Function for a Hydrogenic System (n=7)****Graph Explanation:**The graph displays the radial wave function (N ψ(x)) versus the radial distance (r) for a hydrogenic system with the principal quantum number n = 7. The wave function exhibits oscillatory behavior with peaks and troughs, gradually approaching zero as r increases. The y-axis represents the normalized wave function (N ψ(x)) and ranges from -0.1 to 0.3, while the x-axis represents the radial distance (r) ranging from 0 to 200.**Questions:**a. What is the angular momentum letter of the orbital? - [Text box for answer]b. What is the numerical value of the magnitude of the orbital angular momentum? For \( h \), use the value \( 1.0545718 \times 10^{-34} \) Js. - [Text box for answer] Jsc. What are the possible values of the quantum number for the z-component of the orbital angular momentum? Enter as a comma-separated list from least to greatest (e.g., ..., -1, 0, 1, 2, ...). - [Text box for answer]d. Is there a difference in the electron’s energy if it were in a 4p orbital instead of the orbital it is actually in as indicated by the above wave function? - [Radio buttons for answer] - [ ] yes - [ ] no

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered. The potential energy experienced by an electron in a hydrogen atom is given by Vr=-e24πε0r The Schrodinger equation for the hydrogen atom is given by -ħ22μ∇2ψ+Vrψ=Eψ μ is the reduced mass of the system. The Schrodinger equation is actually given as -ħ22μ1r2ddrr2ddr+1r2sinθddθsinθddθ+1r2sin2θd2dϕ2-e24πε0rψ=Eψ A rigorous calculation can be performed to solve this differential equation by separation of variables and the most important part is the radial wave function. The final wave function depends on n, l and ml. They are principle, azimuthal, and the magnetic quantum numbers (z component of angular momentum) respectively. When a plot of the radial wave function is drawn, it is independent of the magnetic quantum number but dependent on the principle and azimuthal quantum number. The number of nodes of the plot is given by number of nodes =n-l-1 The angular momentum of the electron in lth orbital is given by L=ll+1ħ The magnetic quantum number ml can have many values. The values of ml range from -l to +l with +1 increasing. That means ml=-l, -l+1, -l+2, ...., l-2, l-1, la. In the given plot of the radial wave function we have n=7. From the plot we can see that the number of nodes (where the function is zero) in the radial wave function is 4. Therefore No. of nodes =n-l-1 This gives 4=7-l-1⇒4=6-l⇒l=6-4=2 The letter corresponding to l=2 is d. b. The angular momentum is given by L=ll+1ħ Therefore for l=2 we have L=22+1×ħ=6×1.0545718×10-34Js=2.5831628×10-34Js c. The possible values of ml are ml=-2, -1, 0, 1, 2Answer: a. The angular momentum letter of the orbital is d. b. The magnitude of angular momentum is L=2.5831628×10-34 Js. c. The third component of angular momentum is ml=-2, -1, 0, 1, 2.

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What is the angular momentum letter of the orbital? What is the numerical value of the magnitude of the orbital angular momentum? For i use the value 1.0545718 x 10-34 Js. Js What are the possible values of the quantum number for the z-component of the orbital angular momentum? Enter as a comma separated list from least to greatest (e.g. .-1,0,1,2,.. ):

What is the angular momentum letter of the orbital? What is the numerical value of the magnitude of the orbital angular momentum? For i use the value 1.0545718 x 10-34 Js. Js What are the possible values of the quantum number for the z-component of the orbital angular momentum? Enter as a comma separated list from least to greatest (e.g. .-1,0,1,2,.. ):