The reason that Ti2+ is purple while Ti4+ is colorless lies in their electronic configurations and the concept of crystal field theory. Let's explore this in detail.
Electronic Configurations:
1. Ti2+ has a configuration of [Ar] 3d2. This means that in its d-orbital, there are two electrons. Electrons in d-orbitals can absorb visible light, leading to electron transitions, which result in color.
2. Ti4+ has a configuration of [Ar] with empty 3d orbitals. Since there are no electrons in the d-orbitals, Ti4+ cannot absorb visible light, thus appearing colorless.
Crystal Field Effect:
The color in transition metal complexes is majorly due to the crystal field splitting of d-orbitals and the transitions of electrons between these split d-orbitals. In Ti2+, the presence of 3d electrons allows such transitions, causing the absorption of certain wavelengths of visible light (particularly green and yellow), and the reflection of other wavelengths (such as red and blue), which we perceive as purple. Conversely, for Ti4+, the absence of d-electrons means no such transitions can occur, thus no color is observable.
Therefore, the correct statement is Ti2+ has 3d2 configuration.
The color of transition metal ions arises due to the d-d transitions when the d-orbitals split in the presence of a ligand field. In the case of Ti\(^2+\), the electronic configuration is \( [Ar] 3d^2 \), and there are unpaired electrons in the 3d orbitals.
These unpaired electrons undergo transitions between the split d-orbitals, absorbing specific wavelengths of light, which gives rise to the purple color. On the other hand, Ti\(^4+\) has the electronic configuration \( [Ar] 3d^0 \), which means there are no d-electrons available to undergo these transitions.
Therefore, Ti\(^4+\) is colorless.
Thus, the correct answer is Ti\(^2+\) has \(3d^2\) configuration.
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will be: