Zn\(^{2+}\) salts are colourless. Why?
Zinc salts, specifically those containing the \( \text{Zn}^{2+} \) ion, are colorless due to their electronic configuration.
The electronic configuration of a \( \text{Zn}^{2+} \) ion is:
\( 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10} \)
This configuration shows a completely filled \( 3d \) subshell, with no unpaired electrons.
In transition metal ions, color typically arises from \( d \rightarrow d \) electronic transitions—when electrons jump between split \( d \)-orbital energy levels by absorbing visible light. However, in \( \text{Zn}^{2+} \), these transitions are not possible because:
As a result, \( \text{Zn}^{2+} \) ions do not absorb visible light, and their salts appear colorless in solution.
The Lineweaver-Burk plot for an enzyme obeying the Michaelis-Menten mechanism is given below.
The slope of the line is \(0.36 \times 10^2\) s, and the y-intercept is \(1.20\) mol\(^{-1}\) L s. The value of the Michaelis constant (\(K_M\)) is ________ \( \times 10^{-3} \) mol L\(^{-1}\) (in integer). [Note: \(v\) is the initial rate, and \([S]_0\) is the substrate concentration]
Consider a Carnot engine with a hot source kept at 500 K. From the hot source, 100 J of energy (heat) is withdrawn at 500 K. The cold sink is kept at 300 K. The efficiency of the Carnot engine is ___________ (rounded off to one decimal place).
For the cell reaction, \[ Hg_2Cl_2 (s) + H_2 (1 \, {atm}) \rightarrow 2Hg (l) + 2H^+ (a=1) + 2Cl^- (a=1) \] The standard cell potential is \( \mathcal{E}^0 = 0.2676 \) V, and \( \left(\frac{\partial \mathcal{E}^0}{\partial T}\right)_P = -3.19 \times 10^{-4} \) V K\(^{-1}\). The standard enthalpy change of the reaction (\( \Delta_r H^0 \)) at 298 K is \( -x \) kJ mol\(^{-1}\). The value of \( x \) is ___________ (rounded off to two decimal places). [Given: Faraday constant \( F = 96500 \) C mol\(^{-1}\)]
Assertion : In a semiconductor diode, the thickness of the depletion layer is not fixed.
Reason (R): Thickness of depletion layer in a semiconductor device depends upon many factors such as biasing of the semiconductor.
Show the refraction of light wave at a plane interface using Huygens' principle and prove Snell's law.