The atomic number of Einsteinium (Es) is 99. The electronic configuration of an element can be determined by following the Aufbau principle, which fills the orbitals in the order of increasing energy.
The configuration for Einsteinium is $[\text{Rn}]5f^{11}6d^07s^2$, where:
$[\text{Rn}]$ represents the electron configuration of the nearest noble gas, Radon (86).
The $5f^{11}$ represents the 11 electrons in the 5f subshell.
The $6d^0$ indicates no electrons in the 6d subshell.
The $7s^2$ indicates the 2 electrons in the 7s subshell.
Thus, the correct answer is (2).
Let \( a \in \mathbb{R} \) and \( A \) be a matrix of order \( 3 \times 3 \) such that \( \det(A) = -4 \) and \[ A + I = \begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix} \] where \( I \) is the identity matrix of order \( 3 \times 3 \).
If \( \det\left( (a + 1) \cdot \text{adj}\left( (a - 1) A \right) \right) \) is \( 2^m 3^n \), \( m, n \in \{ 0, 1, 2, \dots, 20 \} \), then \( m + n \) is equal to:
Let \( ABCD \) be a tetrahedron such that the edges \( AB \), \( AC \), and \( AD \) are mutually perpendicular. Let the areas of the triangles \( ABC \), \( ACD \), and \( ADB \) be 5, 6, and 7 square units respectively. Then the area (in square units) of the \( \triangle BCD \) is equal to: