# Find the voltage needed to accelerate the electron from rest

• 0coffeebean0
In summary, an electron can behave as a wave with a wavelength of 6.4 x 10^-15 m when moving at a speed of 1.1384 x 10^11 m/s. To calculate the voltage needed to accelerate the electron from rest until it reaches this speed, one can use the equation E = eV, where E is the kinetic energy gained by the electron and e is its charge. By setting E equal to the kinetic energy calculated in part (a), one can solve for V. This calculation should take into account special relativity, as the speed of the electron is close to the speed of light.
0coffeebean0

## Homework Statement

An electron moving with a speed v can behave as wave with wavelength 6.4 x 10^-15 m. Given that the mass of electron = 9.1 x 10^-31 kg and the charge of electron is 1.6 x 10^-19 C, find
(a) the speed of v of the electron, and
(b) the voltage needed to accelerate the electron from rest until it acquires the speed v.

## The Attempt at a Solution

(a) wavelength = h / mv
v = h/ (m x wavelength)
= 1.1384 X 10^11 m/s

Noctisdark
You are dealing with non-relativistic electron, right ? In that case i don't see any mistake in (a)
(b) Energy = charge * voltage, can you translate that to kinetic energy and pull a speed out of there ?
[EDIT: In case i wasn't clear, the potential energy which is E = e*V translates to kinetic energyenergy but that fact, e*V = mv^2 /2]

Last edited:
The electron gains kinetic energy when moving at the speed you found. Think of the conservation of energy and from where it gained that energy.

Noctisdark
0coffeebean0 said:

## Homework Statement

An electron moving with a speed v can behave as wave with wavelength 6.4 x 10^-15 m. Given that the mass of electron = 9.1 x 10^-31 kg and the charge of electron is 1.6 x 10^-19 C, find
(a) the speed of v of the electron, and
(b) the voltage needed to accelerate the electron from rest until it acquires the speed v.

## The Attempt at a Solution

(a) wavelength = h / mv
v = h/ (m x wavelength)
= 1.1384 X 10^11 m/s

What is the speed of light? Can you use the rest mass of electron to calculate the momentum? See:
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html

Noctisdark
Noctisdark said:
You are dealing with non-relativistic electron, right ?
Can anything travel with 1.1384 X 10^11 m/s speed?

ehild said:
Can anything travel with 1.1384 X 10^11 m/s speed?
Classically, Yes .

What is the speed of light?
Noctisdark said:
Classically, Yes .
And in reality?

ehild said:
What is the speed of light?

And in reality?
It doesn't, but people before the 19th thought that it was possible either way, you are extremely right, but as a homework he should use special relativity, i think, however sorry for that .

## 1. What is the formula for finding the voltage needed to accelerate an electron from rest?

The formula is V = (m x a)/q, where V is the voltage, m is the mass of the electron, a is the desired acceleration, and q is the charge of the electron.

## 2. How do you determine the mass and charge of an electron?

The mass of an electron is a well-known constant, which is approximately 9.11 x 10^-31 kilograms. The charge of an electron is also a well-known constant, which is approximately -1.6 x 10^-19 coulombs.

## 3. Can the voltage needed to accelerate an electron from rest be negative?

Yes, the voltage can be negative. A negative voltage would result in the electron being decelerated instead of accelerated.

## 4. Does the voltage needed to accelerate an electron from rest depend on the direction of acceleration?

No, the voltage needed to accelerate an electron from rest does not depend on the direction of acceleration. The formula accounts for the direction of acceleration through the charge of the electron.

## 5. How is the voltage needed to accelerate an electron from rest related to its kinetic energy?

The voltage needed to accelerate an electron from rest is directly proportional to its kinetic energy. This means that a higher voltage will result in a higher kinetic energy for the electron.

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