The electrons in a TV tube are accelerated from rest through a potential difference of 18kV. Esimate the speed of the electrons after they have been accelerated by this potential difference.

79515.55

energy=potenial *charge

energy also is 1/2 m v^2

you know potential, mass of electron, and charge on an electron. Solve for velocity

To estimate the speed of the electrons, we can use the concept of energy conservation.

The potential difference of 18 kV represents the electrical potential energy gained by the electrons. This potential energy is converted into kinetic energy as the electrons are accelerated.

The kinetic energy (KE) of an electron can be calculated using the equation:
KE = (1/2) * m * v^2,

where m is the mass of the electron and v is its velocity.

The electrical potential energy (PE) gained by the electrons can be calculated using the equation:
PE = q * V,

where q is the charge of an electron (approximately -1.6 x 10^-19 C) and V is the potential difference (18 kV = 18,000 V).

Since the electrical potential energy (PE) gained is converted into kinetic energy (KE), we can set the two equations equal to each other:

q * V = (1/2) * m * v^2.

Simplifying the equation, we can solve for v:

v = √((2 * q * V) / m).

Substituting the values into the equation:

v = √((2 * (-1.6 x 10^-19 C) * 18,000 V) / (mass of an electron)).

The mass of an electron is approximately 9.11 x 10^-31 kg. Substituting this value:

v = √((2 * (-1.6 x 10^-19 C) * 18,000 V) / (9.11 x 10^-31 kg)).

Calculating this expression will give us the estimated speed of the electrons after being accelerated through a potential difference of 18 kV.

To estimate the speed of the electrons after being accelerated through a potential difference, we can use the concept of energy conservation. When an electron moves through a potential difference, the potential energy is converted into kinetic energy.

The kinetic energy of the electrons can be calculated using the formula:

KE = (1/2)mv^2

Where KE is the kinetic energy, m is the mass of the electron, and v is the velocity.

In this case, the mass of an electron, m, is approximately 9.11 x 10^-31 kg.

To find the velocity, we need to equate the kinetic energy to the potential energy gained by the electrons. The potential energy gained is given by qV, where q is the charge of the electron and V is the potential difference.

The charge of an electron, q, is approximately 1.6 x 10^-19 coulombs.

Now we can set up the equation:

(1/2)mv^2 = qV

Substituting the known values:

(1/2)(9.11 x 10^-31 kg)v^2 = (1.6 x 10^-19 C)(18 x 10^3 V)

Simplifying the equation and solving for v:

v^2 = (2)(1.6 x 10^-19 C)(18 x 10^3 V)/(9.11 x 10^-31 kg)

v^2 = (2)(1.6 x 18)/(9.11) x 10^14 m^2/s^2

v^2 ≈ 6.58 x 10^14 m^2/s^2

Taking the square root of both sides:

v ≈ √(6.58 x 10^14) m/s

v ≈ 8.11 x 10^7 m/s

Therefore, the estimated speed of the electrons after being accelerated through a potential difference of 18kV is approximately 8.11 x 10^7 m/s.