Find the directions in space where the angular probability density for the l = 2, ml = 0 electron in hydrogen has its maxima and minima
Find the directions in space where the angular probability density for the l = 2, ml = 0 electron in hydrogen has its maxima and minima
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Find the directions in space where the angular probability density for the l = 2, ml = 0 electron in hydrogen has its maxima and minima.

Transcribed Image Text:This table presents the wave functions of hydrogen atom electron orbitals, categorized by quantum numbers \( n \), \( l \), and \( m_l \). Each row corresponds to a specific combination of these quantum numbers and provides the expressions for the radial, polar, and azimuthal components of the wave functions.
### Table Columns:
- **\( n \):** Principal quantum number
- **\( l \):** Azimuthal quantum number
- **\( m_l \):** Magnetic quantum number
- **\( R(r) \):** Radial wave function
- **\( \Theta(\theta) \):** Polar angle component
- **\( \Phi(\phi) \):** Azimuthal angle component
### Detailed Entries:
#### \( n = 1 \), \( l = 0 \), \( m_l = 0 \)
- **\( R(r) \):** \( \frac{2}{a_0^{3/2}} e^{-r/a_0} \)
- **\( \Theta(\theta) \):** \( \frac{1}{\sqrt{2}} \)
- **\( \Phi(\phi) \):** \( \frac{1}{\sqrt{2\pi}} \)
#### \( n = 2 \), \( l = 0 \), \( m_l = 0 \)
- **\( R(r) \):** \( \frac{1}{(2a_0)^{3/2}} \left( 2 - \frac{r}{a_0} \right) e^{-r/2a_0} \)
- **\( \Theta(\theta) \):** \( \frac{1}{\sqrt{2}} \)
- **\( \Phi(\phi) \):** \( \frac{1}{\sqrt{2\pi}} \)
#### \( n = 2 \), \( l = 1 \), \( m_l = 0 \)
- **\( R(r) \):** \( \frac{1}{\sqrt{3}(2a_0)^{3/2}} \frac{r}{a_0} e^{-r/2a_0} \)
- **\( \Theta(\theta) \):** \( \sqrt{\frac{3}{2}} \cos \theta \)
- **\( \Phi(\phi) \):** \( \frac{
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