How many electrons emerge per second?

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In summary, an ampere is a unit of current and the definition of an ampere is how many electrons per second.
  • #1
Ithryndil
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Homework Statement



The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius 1.20 mm.
(a) The beam current is 7.75 µA. Find the current density in the beam assuming it is uniform throughout.
correct check mark A/m2

(b) The speed of the electrons is so close to the speed of light that their speed can be taken as 300 Mm/s with negligible error. Find the electron density in the beam.
correct check mark m-3

(c) Over what time interval does Avogadro's number of electrons emerge from the accelerator?
s



Homework Equations



[tex]J=I/A[/tex]
[tex]I_{avg} = nqv_{d}A



The Attempt at a Solution



Part a and b are straight forward.

For part a I have: 1.71 A/m^2

For part b I have: 3.565 x 10^10 m^-3

I am having issues with part c. I know I need to figure out how many electrons are leaving the wire per second and then from there it should be a straight division problem using the 6.022 x 10^23 for Avogradro's number.
 
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  • #2
Ithryndil said:

Homework Statement



The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius 1.20 mm.
(a) The beam current is 7.75 µA. Find the current density in the beam assuming it is uniform throughout.
correct check mark A/m2

(b) The speed of the electrons is so close to the speed of light that their speed can be taken as 300 Mm/s with negligible error. Find the electron density in the beam.
correct check mark m-3

(c) Over what time interval does Avogadro's number of electrons emerge from the accelerator?
s

Homework Equations



[tex]J=I/A[/tex]
[tex]I_{avg} = nqv_{d}A[/tex]

The Attempt at a Solution



Part a and b are straight forward.

For part a I have: 1.71 A/m^2

For part b I have: 3.565 x 10^10 m^-3

I am having issues with part c. I know I need to figure out how many electrons are leaving the wire per second and then from there it should be a straight division problem using the 6.022 x 10^23 for Avogradro's number.

Think of it as a bucket. How long to fill'er up.

So what's the definition of an ampere?
 
  • #3
Right...an ampere is a coulomb per second. So we take the current which is a coulomb per second and divide it by the elementary charge to get the number of electrons per second. Afterwards it's a simple division of avogadro's number by the aforementioned number...far easier than I anticipated. Sometimes your mind can just be clouded.
 

FAQ: How many electrons emerge per second?

What is Avogadro's Number and why is it important in science?

Avogadro's Number, also known as the Avogadro constant, is a fundamental constant in chemistry and physics. It represents the number of particles in one mole of a substance, which is approximately 6.022 x 10^23. This number is important because it allows us to easily convert between the mass of a substance and the number of particles it contains, making it a crucial tool in chemical calculations.

How was Avogadro's Number determined?

Avogadro's Number was first determined by Italian scientist Amedeo Avogadro in the early 19th century. He proposed that equal volumes of gases at the same temperature and pressure contain the same number of particles, now known as Avogadro's Law. The value of Avogadro's Number was later refined through experiments such as the oil drop experiment by Robert Millikan and the X-ray crystallography of crystals by Jean Perrin.

What is the relationship between Avogadro's Number and the mole?

The mole is a unit of measurement used in chemistry to represent a specific amount of a substance. It is defined as the amount of a substance that contains the same number of particles as there are atoms in 12 grams of carbon-12. This number of particles is equivalent to Avogadro's Number, so one mole of a substance contains 6.022 x 10^23 particles.

How is Avogadro's Number used in the study of current?

Avogadro's Number is used in the study of current through the concept of the Faraday constant. This constant represents the amount of electrical charge carried by one mole of electrons, which is equal to Avogadro's Number multiplied by the charge of one electron. It is a crucial value in electrochemistry, as it allows us to calculate the amount of charge needed to produce a certain amount of chemical change.

What is the significance of Avogadro's Number in the development of the atomic theory?

Avogadro's Number played a significant role in the development of the atomic theory, which states that all matter is composed of tiny, indivisible particles called atoms. By determining the number of particles in a given amount of a substance, scientists were able to make more accurate measurements and calculations related to the properties of atoms and molecules. Avogadro's Number also helped to solidify the concept of the mole and the idea of counting atoms and molecules in a measurable way, laying the foundation for modern chemistry.

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