Question

An electron with an initial speed of 660,000 m/s is brought to rest by an electric field. What was the initial kinetic energy of the electron, in electron volts?

Answer 1

To find the initial kinetic energy of an electron brought to rest by an electric field, one should first calculate the kinetic energy in joules using the formula KE = (1/2)mv^2, where m is the mass of the electron and v is its speed, then convert the result to electron volts using the conversion factor that 1 eV equals 1.602 × 10^-19 joules.

Step-by-step explanation:

To calculate the initial kinetic energy of an electron in electron volts (eV), you will need to use the formula for kinetic energy (KE) and the conversion factor from joules to electron volts. The formula for kinetic energy is KE = (1/2)mv^2, where m is the mass of the electron and v is the speed of the electron. Since the mass of an electron is 9.11 × 10^-31 kg and it has an initial speed of 660,000 m/s, you can plug these values into the formula to get the kinetic energy in joules.

After calculating the kinetic energy in joules, you can convert it to electron volts by using the factor that 1 eV is equal to 1.602 × 10^-19 joules. The initial kinetic energy in electron volts is then found by dividing the calculated kinetic energy in joules by this conversion factor.

Let's do the calculations:

First, calculate the kinetic energy in joules: KE = (1/2) × (9.11 × 10^-31 kg) × (660,000 m/s)^2.

Next, convert the kinetic energy to eV: KE (in eV) = KE (in joules) / (1.602 × 10^-19 joules/eV).

After performing these calculations, you'll obtain the initial kinetic energy of the electron in electron volts.

Answer 2

Kinetic energy of the electron
`E_k=1.23\ eV`

Step-by-step explanation:

It is given that,

Initial speed of an electron, u = 660000 m/s

Final speed of the electron, v = 0 (at rest)

The kinetic energy of an electron is possessed due to the motion of an electron. The mathematical formula for the kinetic energy is given by :

`E_k=(1)/(2)mv^2`

m is the mass of electron

`E_k=(1)/(2)* 9.1* 10^(-31)* (660000)^2`

`E_k=1.98* 10^(-19)\ J`

Since,
`1\ eV=1.602* 10^(-19)\ J`

`E_k=(1.98* 10^(-19))/(1.602* 10^(-19))`

`E_k=1.23\ eV`

So, the initial kinetic energy of the electron is 1.23 eV. Hence, this is the required solution.