Surfaces, Interfaces and Colloids Questions and Answers

Answer: B

The change is due to the size quantization effect.

In semiconductor nanoparticles (quantum dots) smaller than the exciton Bohr radius, the electron and hole are confined in all three dimensions. Their energy levels become discrete and the effective band gap widens as the particle shrinks, roughly as 1/r² (Brus equation). The absorption edge and λ_max therefore shift systematically with size: to shorter wavelength for smaller particles. This is the quantum size (quantum confinement) effect.

Surface plasmon resonance is the collective oscillation of free electrons in metal nanoparticles such as gold and silver, not semiconductors. 'Nano-effect' is not a defined phenomenon, and bulk band theory by itself predicts a size-independent band gap.

Answer: A

The blue shift is correlated to decrease in size of nanoparticles.

In semiconductor nanoparticles, quantum confinement makes the effective band gap larger as the particle gets smaller. A larger gap means absorption at higher energy, that is, at shorter wavelength. So the spectra moving towards the blue, as the arrow shows, are those of progressively smaller particles.

Larger particles would shift the absorption to longer wavelength (a red shift), towards the bulk band gap. Surface plasmon resonance belongs to metal nanoparticles, not semiconductors, and the shift has everything to do with size.

Answer: A

The matching is A ≡ D, B ≡ E, C ≡ F, option A.

Surface pressure rises when the film is compressed to the area the molecules need. Stearic acid (D) is a straight chain, packs tightly and so gives a steep rise at the smallest area, the vertical curve A. Isostearic acid (E) has a branched end, so each molecule occupies more area before the pressure rises, giving curve B further right. Tri-p-cresyl phosphate (F) is bulky and three-armed with no long chain to align, so it needs the largest area, curve C.

The other options put the bulky molecule at the steep curve or the straight chain at the largest-area curve, which reverses the relation between molecular shape and the area per molecule.

Answer: C

A horizontal line means 1/n = 0.

Taking logarithms of the Freundlich equation gives a straight line:

\[ \log\frac{x}{m} = \log k + \frac{1}{n}\log c \]

The slope of the plot of log(x/m) against log c is 1/n. A horizontal line has zero slope, so 1/n = 0, meaning that the amount adsorbed no longer depends on concentration: the surface is saturated.

The plot is drawn over a range of c, so c is neither zero nor constant; and 'C = 1/n' confuses the variable with the slope.

Answer: C

The isotherm is \(1/V = 1/(PbV_{m}) + 1/V_{m}\), the linear form of the Langmuir isotherm.

The Langmuir isotherm gives the fraction of sites covered as \(\theta = bP/(1 + bP)\). With \(\theta = V/V_{m}\):

\[ \begin{aligned} \frac{V}{V_{m}} &= \frac{bP}{1 + bP} \\ \frac{V_{m}}{V} &= 1 + \frac{1}{bP} \\ \frac{1}{V} &= \frac{1}{V_{m}} + \frac{1}{PbV_{m}} \end{aligned} \]

A plot of 1/V against 1/P is therefore a straight line with intercept 1/V_m and slope 1/(bV_m). The other options misplace V and V_m, so they do not follow from the Langmuir expression.

Answer: B

The sharp absorbance is due to oscillation of free electrons on the metal surface, the surface plasmon resonance.

In silver and gold nanoparticles, light drives the conduction electrons into a collective oscillation at the particle surface. At the resonance frequency this localised surface plasmon gives a strong, sharp band, near 400 nm for silver (yellow sols) and near 520 nm for gold (red sols). The band position shifts with particle size and shape.

Lattice phonons absorb in the infrared, size quantisation dominates in semiconductor quantum dots and very small clusters, and interaction among particles (aggregation) broadens and shifts the band rather than causing it.