A radioactive source is freshly prepared. It is found that it emits radiation of intensity which is 128 times the premissible safe level. The half life of this sample is 3 hours. Find the minimum time after which it would be possible to work safely with this radioactive source.

A current through a wire varies with time, as \( I = \alpha t + \beta t^2 \) where \( \alpha = 10 \, \text{A s}^{-1} \) and \( \beta = 4 \, \text{A s}^{-2} \). How much charge will cross through a section of the wire in 12 s?

A displacement current of 1.0 A is established in the space between the two parallel plates of 1 \( \mu\text{F} \) capacitor. The rate of change of voltage across the capacitor is:

A transmitting antenna at the top of a tower has a height 18 m and the height of the receiving antenna is 32 m. What is the maximum distance between them for satisfactory communication in line-of-sight mode? Given radius of earth is \( 6.4 \times 10^6 \text{ m} \)

In the figure, there are three infinitely long thin sheets having surface charge density \( +3\sigma, -2\sigma \) and \( +\sigma \) respectively. Determine magnitude and direction of the electric field at point A.

A slab of material of dielectric constant \( k \), having the same area as the plate of a parallel plate capacitor but has a thickness \( \frac{3}{5} \) of the distance between the plates \( d \), is inserted between the plates of the capacitor. When there is air between the plates, the potential difference is \( V_0 \). What is the potential difference between the plates of the capacitor after inserting the dielectric?

An electron is accelerated through a potential difference of \( V = 36 \text{ V} \). The de-Broglie wavelength associated with it will be

The function \(f(x)=-2 x^3-9 x^2-12 x+5\) is :

If the de Broglie wavelengths for a proton and an \(\alpha\)-particle are equal, then the ratio of their velocities respectively will be :

The capacitance of a capacitor becomes \( \frac{9}{7} \) times of its original value when a dielectric slab of thickness \( t = \frac{d}{4} \) is inserted between the plates, where d is the separation between the plates. The dielectric constant of the slab is

In the electromagnetic spectrum, the visible spectrum lies between :

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C work together but pipe C is closed after 10 hours, then the time taken by pipe A and B to fill the remaining tank is:

Werner was the first to describe the bonding features in coordination compounds. But his theory could not answer basic questions like :
(i) Why only certain elements possess the remarkable property of forming coordination compounds ?
(ii) Why the bonds in coordination compounds have directional properties ?
(iii) Why coordination compounds have characteristics magnetic and optical properties ?
Many approaches have been put forth to explain the nature of bonding in coordination compounds viz. Valence Bond Theory (VBT), Crystal Field Theory (CFT), Ligand Field Theory (LFT) and Molecular Orbital Theory (MOT).
We shall focus our attention on elementary treatment of the application of VBT and CFT to coordination compounds.
According to this theory, the metal atom or ion under the influence of ligands can use its ( \(n -1\) )d, ns np or ns, np, nd orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on.
These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding.
Which of the following pair of ions is colourless according to CFT ?