# Relating final speed of electron to its charge mass and voltage difference

• franbella
In summary, The speed of the electrons is v, and is calculated to be 6.8 x 10-1 eV s-1 after passing through a voltage difference of 120 kV.
franbella
Assuming that the speed of the electrons is zero as they are emitted from the filament and that as they reach the anode it is v, find an expression relating the final speed v to the charge on an electron, the mass of an electron and deltaV, and hence calculate the speed v of the electrons after passing through a voltage difference of 120 kV.

I'm new to this, but the equation I have come up with is
v = √ 2QΔV
m

I then get this:

√ 2 x (1.602 x 10-19J) x (120-0 x 103eV) = √ 3.8448 x 10-14
8.2 x 10-14 J 8.2 x 10-14 J
√0.46887804 = 0.6847466977
To two significant figures and in scientific notation this is 6.8 x 10-1 eV s-1

You should divide by the mass under the square root, and do care about the units.

Sorry, my first post doesn't make it look like this because my m is not under the square root, but it should be - just an error with copy and paste. So I did do this, but I still feel lost. Is the equation I'm using applicable - the number's I've come up with don't seem right.

i noticed that in your original formula you put the m. What i meant was that when you put in the numbers i don't see you dividing by m.

franbella said:
of the electrons after passing through a voltage difference of 120 kV.

I'm new to this, but the equation I have come up with is
v = √ 2QΔV
m

I then get this:

√ 2 x (1.602 x 10-19J) x (120-0 x 103eV)

Little hard to see from post but remember to change kV into V and charge is in C. Therefore C x V = J, base units of J= kg m2 s-2.

kg m2 s-2
kg

= m2 s-2

square root of m2 s-2 = m s-1

Hope this helped.

Thank you - good reminder - I always forget. Think am getting somewhere now.

## 1. How is the final speed of an electron related to its charge, mass, and voltage difference?

The final speed of an electron can be determined using the equation: v = √(2qV/m), where v is the final speed, q is the charge of the electron, V is the voltage difference, and m is the mass of the electron.

## 2. How does the charge of an electron affect its final speed?

The charge of an electron plays a significant role in determining its final speed. According to the equation, the final speed is directly proportional to the charge of the electron. This means that as the charge of the electron increases, its final speed also increases.

## 3. What role does mass play in determining the final speed of an electron?

The mass of an electron is inversely proportional to its final speed. This means that as the mass of the electron increases, its final speed decreases. Therefore, electrons with a smaller mass will have a higher final speed compared to those with a larger mass.

## 4. Can the voltage difference affect the final speed of an electron?

Yes, the voltage difference plays a crucial role in determining the final speed of an electron. As the voltage difference increases, the final speed of the electron also increases. This is because the voltage difference provides the energy needed to accelerate the electron.

## 5. How does the final speed of an electron relate to its kinetic energy?

The final speed of an electron is directly related to its kinetic energy. As the final speed of the electron increases, its kinetic energy also increases. This is because the kinetic energy of an object is directly proportional to its velocity.

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