Please help with this question. thanks! In laser cooling and trapping the forces

Question

Please help with this question.

thanks!

In laser cooling and trapping the forces associated with radiation pressure are used to slow down atoms from thermal speeds of hundreds of meters per second at room temperature to speed of a few meters per second or slower. An isolated atom will absorb only radiation of specific frequencies. If the frequency of the laser beam radiation is tuned so that the target atoms will absorb the radiation, then the radiation is absorbed during a process called resonant absorption. The cross sectional area of the atom for resonant absorption is approximately equal to 12, where is the wavelength of the laser light. Estimate the acceleration of a rubidium atom (molar mass 85 g/mol n a laser beam whose wavelength is 790 nm and intensity is 9.0 w/m^2 1.32e+05 m/s^2 About how long would it take such a light beam to slow a rubidium atom in a gas at 290 K to near zero speed? _________ ms

Explanation / Answer

b)

intitial velocity = 3 kT/m = 3*1.3807*10^-23*290/(85*10^-3*1/(6.023*10^-23)) = 85116.2566 m/s

The final velocity = 0

acceleration = 1.32*10^5 m/s^2

hence the time taken t = (v_i - v_f)/a

t = 85116.2566/(1.32*10^5) = 0.645 sec. = 645 ms.

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