Question

In electron spin resonance (ESR) and nuclear magnetic resonance (NMR), the energy levels of electrons or protons, respectively, are split with a magnetic field (otherwise known as the Zeeman effect). Electrons or protons with spin in the same direction as the magnetic field have lower energies than electrons or protons with spins aligned opposite to the field. The energy difference between these levels depends on the strength of the field, so ESR and NMR can be used to measure, very precisely, the strength of the magnetic field at the location of these particles. (Knowing the magnetic field, then, can be used to determine the physical environment of these particles. For example, in ESR, free radicals produced by radiation provides information about the mechanisms of radiation damage. Magnetic field-induced energy splits in NMR can be used to determine, e.g., the structure of different compounds.)

In a particular ESR experiment, a spin doublet is created for which the decay of an electron in a lower energy spin state emits longer wavelength radiation while an electron in the higher energy spin state emits shorter wavelength radiation. On a screen 10 cm from a grating which splits the radiation of different wavelengths, the first interference maximum of the shorter wavelength radiation lies 3.00 cm from the center of the screen whereas the first interference maximum of the longer wavelength radiation lies 3.01 cm from the center of the screen. If the shorter wavelength is 510 nm, what is the longer wavelength (in nm, to the nearest tenth of a nm)?

Answer 1