# Voltage is the speed of electricity

### Accelerating voltage

### Subject matter

Electric voltage, electric charge. Elemental charge. Kinetic energy.

learning goals

### task

Electrons emerge from a hot cathode (negative pole) and move to the anode (positive pole). In doing so, they are attracted to the anode; the electrons are accelerated.

Calculate how the final velocity of the electrons depends on the voltage U, the elementary charge e = 1.6 · 10^{-19} C and the electron mass m = 10^{-30} depend on kg! Justify the following reshaping steps and check by clicking on the "Tip"!

From the voltage U = W / e we calculate the increase in kinetic energy:

E._{kin} = e U (tip)

m · v^{2} / 2 = e * U

v^{2} = 2 e rev / m (tip)

**Result:** v = √ (2 e U / m)

Calculate the velocity v that electrons get after passing through a certain accelerating voltage with the following form!

**Note:** The above formula only applies to "classical conditions" - the speed of the electrons must be well below the speed of light c_{0} = 3 · 10^{8} m / s = 300 x 10^{6} m / s lie (**classical approximation**).

Compare your results with c_{0}! Up to which acceleration voltage does it make sense to calculate "conventionally"?

### activities

Where are "individual electrons" accelerated in technical devices? Research applications from research and technology!

- Calculate the final speed of the accelerated electrons for different voltages (eg: U = 350 V, U = 5 kV, U = 8 kV, U = 20 kV)!
- Does twice the acceleration voltage lead to twice the speed of the electrons?
- Compare the final speed of electrons with the speeds of heavier particles that are accelerated at the same voltage! For example, what can you do for protons (m = 10
^{-27}kg) testify? - When fast electrons hit an obstacle, X-rays are generated. Research the acceleration voltages from which X-rays can occur!
- At high speeds, relativistic effects must be taken into account (cf. 20 Relativity). Research the connections in this "non-classical case"!

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