Fluorescence microscopy, discussed in Section 29.8, is an important tool in modern cell biology. A variation on this technique depends on a phenomenon known as two-photon excitation.If two photons are absorbed simultaneously (i.e., withinabout 10-16 s), their energies can add. A molecule that is normallyexcited by a 350 nm photon can be excited by two photonseach having half as much energy. For this process to beuseful, photons must illuminate the sample at the very high rateof at least 1029 photons/m2 # s. This is achieved by focusing alaser beam to a small spot and by concentrating the power ofthe laser into very short 110-13 s2 pulses that are fired 108 timeseach second. Suppose a biologist wants to use two-photon excitationto excite a molecular species that would be excited by500 nm light in normal one-photon fluorescence microscopy.What minimum intensity 1W/m2 2 must the laser beam haveduring each pulse?

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Fluorescence microscopy, discussed in Section 29.8, is an important tool in modern cell biology. A variation on this technique depends on a phenomenon known as two-photon excitation.
If two photons are absorbed simultaneously (i.e., within
about 10-16 s), their energies can add. A molecule that is normally
excited by a 350 nm photon can be excited by two photons
each having half as much energy. For this process to be
useful, photons must illuminate the sample at the very high rate
of at least 1029 photons/m2 # s. This is achieved by focusing a
laser beam to a small spot and by concentrating the power of
the laser into very short 110-13 s2 pulses that are fired 108 times
each second. Suppose a biologist wants to use two-photon excitation
to excite a molecular species that would be excited by
500 nm light in normal one-photon fluorescence microscopy.
What minimum intensity 1W/m2 2 must the laser beam have
during each pulse?

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