Zn\(^{2+}\) salts are white while Cu\(^{2+}\) salts are blue in colour. Why?
Step 1: Electronic Configurations: - Zn\(^{2+}\) = \(3d^{10}\) (fully filled, no d-d transitions)
- Cu\(^{2+}\) = \(3d^9\) (one unpaired electron, d-d transitions possible)
Step 2: Reason for Colour: - Zn\(^{2+}\) has no unpaired d-electrons → No d-d transitions → Appears white.
- Cu\(^{2+}\) has d-d transitions absorbing red-orange light, reflecting blue.
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $