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a) If a photon and an electron each have the same energy of 20.0 eV, find the wavelength of each.

b) If a photon and an electron each have the same wavelength of 250 nm, find the energy of each.
c) You want to study an organic molecule that is about 250 nm long using either a photon or an
electron microscope. Approximately what wavelength should you use and which probe, the electron or
the photon, is likely to damage the molecule least?

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  1. (a) For the electron,
    E = 3.2*10^-18 J
    momentum = sqrt(2m*E)
    = 2.41*10^-24 kg m/s
    wavelength = h/(momentum) = 2.74*10^-10 m

    For the photon, the energy is the same but
    wavelength = h*c/(Energy)
    = 6.2*10^-8 m

    (b) Use the formulas

    E(photon) = h*c/(wavelength)
    E(electron) = (momentum)^2/(2*Mp)
    = [h/(wavelength)]^2/(2*Mp)
    where Mp is the proton mass.

    (c) Pick the microscope that uses particles of least energy, for a given wavelength. The wavelength determines the resolving power.
    Wavelength and resolution element size are roughly the same. Look up the appropriate formulas online.

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