# How to form a molecular beam?

Often, the molecules used in the experiments are available as a powder. Neutrons, protons and electrons form atoms which are, in turn, combined to molecules of different sizes.
In order to study their wave nature, we need a beam of single objects. They have to be electrically neutral so as to avoid deflection by uncontrolled electrical fields.

## Phase change

To form such a beam we heat the molecules in a special oven (Knudsen cell) inside the vacuum chamber. There they sublimate or evaporate into the gas phase, leave through a small orifice and fly through the experiment. The oven consists of a ceramic vessel around which a heating wire is wound. Passing electrical current through the wire heats the ceramic vessel.

If one wants to heat the oven quickly and effectively heat losses need to be minimized.

## Transfer of heat

The low pressure in the vacuum chamber avoids any heat loss by convection. Due to the narrow suspension of the oven, heat loss caused by conduction to the vacuum chamber is minimized. The greatest loss is caused by thermal radiation. To minimize this loss, the oven is surrounded by a sheet of tantalum that reflects a large part of the heat radiation.

To get a sufficiently intense molecular beam, the vapour pressure inside the oven needs to be high enough. For this, different types of molecules need different temperatures. C-60-fullerenes are heated to 600°C – 700°C, Carotene only to 200°C – 240°C.

The vapour pressure as well as the velocities of the particles increase with the temperature. The velocities can be described fairly accurately with a Maxwell-Boltzmann distribution.

Extra: The Maxwell-Boltzmann distribution

The Maxwell-Boltzmann distribution gives the probability $$p(v)$$ for each velocity $$v$$ with the function:

$$p(v) \mathrm{d}v = 4\pi \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 \exp\left(-\frac{m v^2}{2k_B T}\right) \mathrm{d}v$$

The most probable velocity $$\hat{v}$$ is given by:

$$\hat{v}=\sqrt{\frac{2 \cdot k_B \cdot T}{m}}$$,

with the Boltzmann constant $$k_B$$, the absolute temperature $$T$$ in $$\mathrm{K}$$, and the mass $$m$$ in $$\mathrm{kg}$$.

Now, consider the temperature and the mass; how do they influence the velocity of the molecules?

 Mass $$m$$ - + Temperature $$T$$ - +

You can also study this in the simulation below. You can change the temperature and observe how it influences the velocity of the molecules.

 cool / heat

## Maxwell-Boltzmann Distribution

The molecules leave the oven nozzle with $$I(\theta) = I_0 \cdot \cos(\theta)$$.
$$I_0$$ is the intensity in the forward direction and $$\theta$$ the exit angle.