d. Compute the numerical value of the integral 2 Rn, (r)' Rn,(r) dr : Enter a number.
d. Compute the numerical value of the integral 2 Rn, (r)' Rn,(r) dr : Enter a number.
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D
![**Radial Wave Function for the 5f Orbital**
The radial wave function for the 5f orbital can be expressed as:
\[ R_{n,l}(r) = N \, e^{-r/5} \, r^3 \left(8 - \frac{2r}{5}\right) \]
where \( N \) is a normalization constant.
**Exercises:**
a. **What is \( n \)?**
\( n = \) \( \boxed{5} \)
b. **What is \( l \)?**
\( l = \) \( \boxed{3} \)
c. **How many nodes does this wave function have?**
\(\# \text{ of nodes} = \) \( \boxed{1} \)
d. **Compute the numerical value of the integral**
\[
\int_{0}^{\infty} r^2 \, R_{n,l}(r) \cdot R_{n,l}(r) \, dr =
\]
\(\boxed{\text{Enter a number.}}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0bb33da-4292-4a51-8799-113a66f1981e%2Fa8b9f6da-a765-4c5e-a9c5-2ac844e11042%2Fo29l0ml_processed.png&w=3840&q=75)
Transcribed Image Text:**Radial Wave Function for the 5f Orbital**
The radial wave function for the 5f orbital can be expressed as:
\[ R_{n,l}(r) = N \, e^{-r/5} \, r^3 \left(8 - \frac{2r}{5}\right) \]
where \( N \) is a normalization constant.
**Exercises:**
a. **What is \( n \)?**
\( n = \) \( \boxed{5} \)
b. **What is \( l \)?**
\( l = \) \( \boxed{3} \)
c. **How many nodes does this wave function have?**
\(\# \text{ of nodes} = \) \( \boxed{1} \)
d. **Compute the numerical value of the integral**
\[
\int_{0}^{\infty} r^2 \, R_{n,l}(r) \cdot R_{n,l}(r) \, dr =
\]
\(\boxed{\text{Enter a number.}}\)
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