A group of atoms is confined to a very small (point like) volume in a laser-base

Question

A group of atoms is confined to a very small (point like) volume in a laser-based atom trap. The incident laser light causes each atom to emit 1.6 times 10^6 photons of wavelength 680 nm every second. A sensor of area 1.6 cm^2 measures the light intensity emanating from the trap to be 3.0 n W when placed 20 cm away from the trapped atoms. Assuming each atom emits photons with equal probability in all directions, determine the number of trapped atoms. Express your answer using two significant figures. N = 2.0 times 10^7 atoms

Explanation / Answer

= A / (4 R2) = 1.6 / (4 * 202) = 3.18 * 10-4 fractionof total energy received at detector

Ep = h c / = 6.63 * 10-34 * 3 * 108 / 6.8* 10-7 = 2.92 * 10-19 J    energy perphoton

Pa = 1 * 10E6 * Ep = 2.92 *10-13     power emitted by each atom

N Pa = 3*10-9       power received atdetector from N atoms

N = 3* 10E-9 / (2.92 * 10-13 * 3.18 * 10-4) = 3.23* 107atoms

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