Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section B / 38

The binding energies are referred to the common Fermi level. Immediately outside the copper surface, conservation of energy givesThis is the emitted photoelectron energy at the sample. On reaching the electrically connected, unbiased analyser, its energy is instead $K_a=h\nu -E_B-{\varphi }_a=\boxed{111.4\mathrm{eV}}$. The 0.4 eV difference is the contact-potential correction, not an additional binding-energy shift. Distinguishing these two reference positions is essential for the retarding-voltage calculation.

The hemispherical component needs 100.0 eV electrons, whereas electrons arrive at its entrance optics with 111.4 eV. The optics must therefore remove 11.4 eV, requiring a retarding-potential magnitude of 11.4 V. For a negative electron, moving to a more negative electrostatic potential increases potential energy, so the retarding region is 11.4 V negative relative to the analyser entrance. Equivalently the hemisphere entrance is 11.8 V negative relative to the sample vacuum reference after including the 0.4 V contact step. Reporting 11.8 V as the additional instrument retardation would count the contact correction twice.

Fixed entrance retardation and fixed pass energy select the same pre-retardation kinetic energy, 111.4 eV. The required photon energy is thereforeIt is lower than the original excitation by exactly the difference between the two core binding energies, 114.4 eV.

Define the retard ratio using the kinetic energy at the analyser entrance before the deliberate retardation: $R=K_a/E_p$. Initially $R=111.4/100.0=1.114$. With the original excitation, a carbon photoelectron arrives with $K_{a,C}=515.0-284.8-4.4=225.8\mathrm{eV}$. ThusThe new deliberate retardation is $225.8-202.69=23.11\mathrm{eV}$. For fixed slits, angular acceptance and hemisphere radii, the geometrical fractional energy width is approximately constant, so the absolute analyser width grows in proportion to pass energy: about 2.03 times poorer absolute energy resolution. Counts may improve, but closely separated chemical shifts become harder to resolve. An alternative definition $(K_a-E_p)/E_p$ gives 0.114 rather than 1.114 for the same physical setting and leads to the same final pass energy when used consistently.

The large resonance at the smallest field-to-normal angle identifies an unoccupied orbital whose transition dipole is mainly normal to the surface. An N 1s initial state is approximately spherical; the dipole matrix element for a $1s\to {\pi }^{\ast }$ transition is directed along the normal to the adsorbate's aromatic plane. Consequently the adsorbate rings lie predominantly parallel to the copper surface. For perfectly flat molecules the resonance strength scales as $|\mathbf{E}\cdot \hat{\mathbf{n}}{|}^2\propto {\cos }^2\theta$, which decreases strongly from $17^{\circ }$ to $67^{\circ }$ as observed.

For azimuthally disordered molecular normals tilted by $\alpha$ from the surface normal, averaging gives $I(\theta )\propto {\cos }^2\theta {\cos }^2\alpha +\frac{1}{2}{\sin }^2\theta {\sin }^2\alpha$. Strong dichroism therefore implies a large orientational order parameter, but the plotted qualitative curves alone do not determine a unique tilt angle or distribution. Background subtraction, incident polarization and intensity normalization would be needed for such a fit. This experiment identifies the orientation of the pi system; it does not by itself identify a particular nitrogen–copper bonding topology.

The initial nitrogen environment loses intensity on heating, and a lower-binding-energy component becomes prominent near the highest temperatures. A change of surface chemical species accompanies loss or conversion of the original adsorbate. Plausible processes include thermally activated decomposition with nitrogen-containing fragments remaining on copper, desorption of intact material or fragments, and rearrangement of the coordination environment. The extra components at intermediate temperatures suggest coexistence rather than a rigid, uniform shift of every molecule.

The individual curves have vertical offsets, so their baseline height is not a coverage measurement. Integrated, sensitivity-corrected N and C peak areas, a clean heated substrate control, and evolved-gas mass spectrometry would help distinguish loss of material from chemical conversion. binding energy alone cannot establish a unique fragment structure: local charge, metallic screening and coordination all affect it.