In aqueous solutions, the stability of \(Cu^{2+}\) compared to \(Cu^+\) salts is primarily due to the differences in their hydration energy. Let's explore this concept:
Hydration Energy: When ions dissolve in water, they become surrounded by water molecules. This interaction releases energy, known as hydration energy. The magnitude of hydration energy depends on the charge density of the ion; higher charges and smaller radii lead to higher hydration energies.
Comparison of \(^+\) and \((Cu^{2+}\):
Due to the greater hydration energy of \(Cu^{2+}\), it is more stable than \(Cu^+\) in aqueous solutions. This enhanced stability favors the presence of \(Cu^{2+}\) over \(Cu^+\) in solution, explaining why hydration energy is the key factor in determining the stability.
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :