Force and acceleration on sodium atom if laser bundle shines on atom

[jennyjones]

Homework Statement

I want to calculate the average force and acceleration on an sodium atom, if a laser bundle shines on it
which has I>>>> I(sat). I(sat) is the saturation intensity of the 589nm 3s-3p transition in sodium.
3p lives 16 ns

Homework Equations

c = 3 * 10 ^ 8
m sodium = 3.8 * 10^-26 kg
planck = 6.6* 10 ^-34 Js
tua = 16 ns

The Attempt at a Solution

F = - h(bar)/(2*λ*(tau)) ?

not sure which formula to use


thanx,

jenny

 

[haruspex]

Not an area I know anything about, but the formula you quoted looks almost right to me.
The h/λ part gives you the momentum of each photon. 1/tau, where tau is the remanence time in the excited state, gives you the max rate of excitation. The reradiation is in a random direction, so you should only count the momentum of the absorbed photons. Force equals rate of change of momentum, so momentum per excitation multiplied by rate of excitation events.

What I don't understand is the constant factor of 1/4π. Maybe someone who knows this area will comment.

 

[BvU]

Hello Jenny,

Could you reveal a bit more of the context of your post ?
I am intrigued by the I >> Isat. I take it the laser is tuned to the 589 nm, but the spectral width isn't indicated: is it sharper than the D-line or much broader?

When you irradiate Na atoms, you get resonance fluorescence (in all directions) and you also get stimulated emission (in the same direction as the incoming photon). When the intensity in increased, the latter shortens the residence time in the upper level (power broadening, page 90). Hope this link works, otherwise: Laser Spectroscopy: Vol. 1: Basic Principles
By Wolfgang Demtröder

I seem to recall that with a broadly tuned laser you get line broadening and with a very sharply tune laser you can get line splitting, but I'm not that sure - long time ago.

However, momentum conservation goes: Cohen-Tannoudji and Dalibard -- real experts in this field, the former a Nobel laureate -- mention a recoil of the atom of around 3 cm/s on p 16 . ( ##p = \hbar{\bf k} = h/\lambda##. No ##1/(4\pi)##. The ##1/\tau## comes in as the number of photons that can be absorbed per second, as Haruspex already wrote).

CT & D work out radiation pressure on p 17; more or less what you are asking.

 

[jennyjones]

thanks so much for the help!

i think i know how to solve the problem now!

F = dp/dt = - h/λτ
F = - 6.6* 10 ^-34/(589 * 10^-9 * 16 * 10^-9) = -7 * 10^-20

a = F/m = -7 *10^-20/ 3.8 * 10^-26 kg = -1.8 *10^6

 

[HalfLostAndSearching]

I would first like to clarify that the force and acceleration on a sodium atom will depend on several factors, including the intensity and wavelength of the laser bundle, the size and energy state of the atom, and the surrounding environment. It is not possible to provide a single definitive answer without more specific information.

That being said, I can provide some guidance on how to approach this problem. The formula you have mentioned, F = - h(bar)/(2*λ*(tau)), is known as the "radiation pressure formula" and is often used to calculate the force exerted on an object by a beam of light. However, this formula assumes that the object is perfectly reflective and stationary. Since a sodium atom is neither of those things, it may not be the most appropriate formula to use in this case.

Instead, a more accurate approach would be to consider the interaction between the laser bundle and the electron(s) within the sodium atom. This can be described using quantum mechanics, specifically the Schrödinger equation, which takes into account the energy levels and wavefunctions of the atom. From there, one could calculate the change in momentum and energy of the atom due to the absorption of photons from the laser bundle, and use those values to determine the force and acceleration experienced by the atom.

In summary, the calculation of force and acceleration on a sodium atom under the influence of a laser bundle is a complex problem that requires a thorough understanding of quantum mechanics and the specific parameters of the system. I would recommend consulting with a physicist or conducting further research to determine the most appropriate approach for your specific scenario.