= Solution
The <binding energies> are referred to the common <Fermi level>. Immediately outside the <copper> surface, <conservation of energy> gives
$$
K_s=h\nu-E_B-\phi_s=515.0-399.2-4.0=\boxed{111.8\ \mathrm{eV}}.
$$
This is the emitted <photoelectron> energy at the sample. On reaching the electrically connected, unbiased analyser, its energy is instead $K_a=h\nu-E_B-\phi_a=\boxed{111.4\ \mathrm{eV}}$. 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.
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