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Please explain answers and show formulas used and label units Fluorescent molecu

ID: 1304231 • Letter: P

Question

Please explain answers and show formulas used and label units

Fluorescent molecules can be used to track biomolecular events one molecule at a time.
Fluorescence is very similar to the atomic transitions studied in lecture. Consider a
fluorescent molecule where the electron that participates in fluorescence has ground state energy of
-4.6 eV. When the molecule is illuminated with light this electron is excited up to a state
with energy -2.3 eV.

5) (3 pt) The average time the electron stays in the excited state before dropping back
into the ground state is called its mean lifetime. The fact that the lifetime is not infinite
introduces some uncertainty in the energy of the photon, and thus the wavelength. If the
lifetime of the excited state in this problem is 3 ns, what is the spread of uncertainty in the
wavelength?

Explanation / Answer

energy emitted = hc/ lambda = energy absorbed by photom

or, 2.3 *1.6*10^-19 = 6.6*10^-34 * 3*10^8 / lambda

so, lambda = wavelength of the emitted photons = 5.38 * 10^-7 m

uncertainity in wavelength = deltaE * delta t

= hc/(lambda) * 3*10^-9

= 2.3*1.6*10^-19 *3*10^-9

= 1.104*10^-18 J/s