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Chapter 4: Q. 4.36 (page 148)

An apparent limit on the temperature achievable by laser cooling is reached when an atom's recoil energy from absorbing or emitting a single photon is comparable to its total kinetic energy. Make a rough estimate of this limiting temperature for rubidium atoms that are cooled using laser light with a wavelength of 780 nm.

Short Answer

Expert verified

Limiting temp is 1.2 x 10-7 K

Step by step solution

01

Given Information

Wavelength , 位 =780 nm.

02

Explanation

de Broglie wavelength formula is written as

p=h位

Kinetic energy in terms of momentum , can be written as:

K=p22m

Kinetic energy in terms of temperature can be written as:

K=32kT

K=kinetic Energy
P=momentum
M= mass
k= Boltzmann constant

T=Temperature

Now substitute values and calculate

K=p22m=32kT鈬�p22m=32kT鈬�p23m=k

鈭�p=h位鈬�h位23m=kT鈬�T=h23km位2

鈬�T=6.63脳10-34Js23脳85脳1.66脳10-27kg780脳10-9m21.38064852脳10-23m2kgs-2K-1

So T= 1.2 x 10-7 K

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