# Electrical Breakdown/Avalanche of Air Classical Mechanics Collision Theory

• alimerzairan
In summary, electrical breakdown is caused by an avalanche process. If a free electron gains enough energy between collisions to ionize the neutral molecules when they collide with them, then those two electrons will gain enough energy between collisions to ionize the next neutral molecules they collide with and the ionization of the gas grows exponentially. Conversely, if the electron doesn't gain enough energy to ionize the molecule, it will lose energy in collisions with neutral molecules and will eventually recombine.

## Homework Statement

Electrical breakdown (e.g, lightning) is caused by an avalanche process. If a free electron gains enough energy between collisions to ionize the neutral molecules when they collide with them, then those two electrons will gain enough energy between collisions to ionize the next neutral molecules they collide with and the ionization of the gas grows exponentially. Conversely, if the electron doesn’t gain enough energy to ionize the molecule, it will lose energy in collisions with neutral molecules and will eventually recombine.

(a) Estimate how large the electric field must be for breakdown to occur. The electron needs to gain ∼ 200 eV of energy between collisions and the maximum cross section for ionization of air molecules is about 3 × 10−16 cm2.

(b) If the electric field is large enough for breakdown to occur, estimate how fast the current channel of free electrons forms.

## Homework Equations

V = E d

d = mean free path

## The Attempt at a Solution

V = 200 V since the electron gains 200 eV.
d is calculated by $$\frac{V}{N_{A} \sigma}$$, where $$N_{A}$$ is Avogadro's number and in STP with V = 22.4 x 10-3 m.3.

Don't know if this exactly right. I get d = 1240.3 nm and an electric field for breakdown to occur of $$161.25 \times 10^{6} \frac{V}{m}$$ while I read that it should be around $$3 \times 10^{6} \frac{V}{m}$$.

Also, for part (b) I don't even know what they are asking for.

Any help before Tuesday, January 18 at 1:00 Pacific Time (GMT -0800) would be greatly appreciated.

hi alimerzairan!

(have a theta: θ and a sigma: σ and try using the X2 icon just above the Reply box )

not really my field , but anyway …

you don't seem to have used the cross-section …

it occurs to me that if the electron misses that cross-section, it'll be able to travel further and pick up more energy before its next collision, so the average d will be greater, and E = V/d will be smaller …

does that work?

(btw, did you mean 1:00 am? that's an unusual deadline )

Hi Tiny-Tim,

I do use the cross section for the mean free path, d.

I guess you are not in the United States since we are the only country that still uses a.m. and p.m. when the rest of the world works under 24-hour clock. Don't know why this country doesn't change, but what I mean by 1:00 is 13:00 Pacific time GMT (-0800).

Does anyone understand the second part of the problem. I am primarily stuck on that.

## 1. What is electrical breakdown/avalanche of air?

Electrical breakdown/avalanche of air is a phenomenon where a high voltage electric current causes a sudden and rapid increase in the number of electrons and ions in the air, leading to the creation of an electric arc or spark.

## 2. What causes electrical breakdown/avalanche of air?

Electrical breakdown/avalanche of air is caused by the ionization of air molecules due to the presence of a high voltage electric field. When the electric field exceeds a certain threshold, it causes the air molecules to lose electrons and form ions, which leads to a chain reaction and the creation of an electric arc or spark.

## 3. How does classical mechanics play a role in electrical breakdown/avalanche of air?

Classical mechanics plays a role in electrical breakdown/avalanche of air through its principles of motion and energy conservation. The high voltage electric field creates a force on the air molecules, causing them to accelerate and collide with other molecules. This results in an increase in kinetic energy and temperature, leading to the formation of an electric arc or spark.

## 4. What is collision theory in relation to electrical breakdown/avalanche of air?

Collision theory explains how the high voltage electric field causes the air molecules to collide with each other, leading to the creation of an electric arc or spark. The theory states that for a reaction to occur, the colliding molecules must have enough energy and the correct orientation, which is achieved through the acceleration and collision of air molecules in the electric field.

## 5. How is electrical breakdown/avalanche of air relevant to everyday life?

Electrical breakdown/avalanche of air is relevant to everyday life as it is the basis for many common household appliances, such as spark plugs, fluorescent lights, and electric discharge lamps. It is also a key concept in understanding lightning and other natural phenomena. Understanding this phenomenon is crucial in ensuring the safe and efficient use of electricity in daily life.