Lasers have been developed that can generate pulses of light thatare only 10 fs

Question

Lasers have been developed that can generate pulses of light thatare only 10 fs (femtoseconds) long. Assume lamdar= 500nm (Note: 1fs is 1x10-15s)
(a) How many wavelengths of light are contained in such apulse? (b) If the power during a pulse is 1mW, how much energy (ineV) is contained in each pulse? (c) How many photons are there in each pulse?
(a) How many wavelengths of light are contained in such apulse? (b) If the power during a pulse is 1mW, how much energy (ineV) is contained in each pulse? (c) How many photons are there in each pulse?

Explanation / Answer

PART a >>>>      Thespeed of light c is related to freq f and wavelength by the eqn    c = f   and since f = 1 / T, where T is the period, then weget:                                                            c = ( 1 / T )    or   T = / c = 500 E -9 m / 3 E 8 m/s = 1.67E-15 sec This period T is the time for 1 wavelength to pass a givenpoint. So,   the number of wavelengths in 10 fsis       10 E - 15 sec / 1.67 E -15sec =   5.99 or round to 6 if you wish. PART b>>>>   E = ( P ) (T) = ( 1 E -3 J/sec) (10 E - 15 sec ) = 1 E - 17J / (1.6 E - 19 J / eV ) = 62.5 eV PART c>>>>>    energy of 1photon = h f                                            = (6.6 E - 34 J-sec) ( 1 / 1.67E -15 sec) = 3.95E-19 J /(1.6E-19J/eV) = 2.47 eV number of photons in a pulse = total energy in the pulse /energy of 1 photon = 62.5 eV / 2.47 eV = 25.3 or25

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