The electron drift speed is 2.0 X 10⁻⁴ m/s in a metal with a mean...

Question

The electron drift speed is 2.0 X 10⁻⁴ m/s in a metal with a mean time between collisions of 5.0 x 10⁻¹⁴ . What is the electric field strength?

Accepted Answer

Welcome back everyone in this problem, the electrons in a semiconductor have an average time between collisions of seven picos given an electron moves at a drift speed of 3.5 times 10 to the negative 3 m per second in the semiconductor, determine the magnitude of the electric field. For our answer choices. A is 7.1 times 10 to the negative four volts per meter. B is 3.9 times 10 to the negative eight C is 4.6 times 10 to the negative six and D is 2.8 times 10 to the negative three. And all of those are in units volts per meter. Now let's try and picture what's really going on here. So let's imagine that we are able to look inside the semiconductor. And what's really happening is that we are having electrons that on average are colliding every seven PICO secons. And we know that they are moving at a drift speed of 3.5 times 10 to the negative 3 m per second. And we want to determine the magnitude of the electric field. No, if we think about it, if we think about it right, we're talking about an electric field. What does drift speed have to do with the electric field? How are they related? Well, recall that our drift speed equals our electron mobility multiplied by the strength of the electric field. In other words, our drift speed depends on how mobile our electrons are and how strong our electric field is. So if we want to find the strength of our electric field, we can divide the drift field, the drift speed by our electron mobility. Now we know our drift speed. But the question is how can we tell how mobile or electrons are? Well, also recall that electron mobility equals e multiplied by tat divided by M where E represents the charge of an electron tort represents the average time between collisions and M represents the mass of an electron. And we can have that information because we know that the charge of an electron equals 1.6 times 10 to the negative 19 coulombs. We know that our average time between collisions has been given as seven PICO secons. So that would be seven oops seven times 10 to the negative 12 seconds. OK. And we also know that the mass of an electron mass of an electron equals 9.1 times 10 to the negative 31 kg. So since we have this information, we should be able to substitute our value for electron mobility into our formula to solve for the strength of an electric field. So let's do that. So solving for strength of our electric field magnitude for electric field, E would be equal to our drift speed divided by mu which is E tat divided by M. If we rewrite that, then we'll get our magnitude of our electric field to be just speed multiplied by the mass divided by E thought. No, we just need to plug in the values. So the magnitude of our electric field equals our drift speed, which is 3.5 times 10 to the negative 3 m per second, multiplied by the mass of an electron which is 9.1 times 10 to the negative 31 kilograms. And all of that is being divided by the charge of an electron which is 1.6 times 10 to the negative 19 coulombs multiplied by the average collision time, which is seven times 10 to the negative 12 seconds. So this equation will give us the magnitude of our electric field. Let's plug these values into our calculator. When you do that, you should find that the strength of the electric field equals 2.8 times 10 to the negative three volts per meter to the nearest decimal place. So that means the magnitude of the electric field is approximately 2.8 times 10 to the negative three volts per meter. When we go back to our answer choices, that would have been answer choice. D thanks a lot for watching. Everyone. I hope this video helped.

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The electron drift speed is 2.0 X 10⁻⁴ m/s in a metal with a mean time between collisions of 5.0 x 10⁻¹⁴ . What is the electric field strength?

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