The number of radial nodes for an orbital is given by the formula:
Number of radial nodes = n − l − 1
where: - n is the principal quantum number. - l is the azimuthal quantum number
(orbital angular momentum quantum number).
For a 3p orbital: - n = 3 - l = 1 (since it is a p-orbital)
Applying the formula:
Number of radial nodes = 3 − 1 − 1 = 1
Conclusion: The number of radial nodes for the 3p orbital is 1.
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: