A 9V battery has an electric potential difference of 9V between the positive and negative terminals. How much kinetic energy in J would an electron gain if it moved from the negative terminal to the positive one?

Question

A 9V battery has an electric potential difference of 9V between the positive and negative terminals. How much kinetic energy in J would an electron gain if it moved from the negative terminal to the positive one?

Answer 1

To determine the kinetic energy gained by an electron moving from the negative terminal to the positive terminal of a 9V battery, we need to understand the relationship between electric potential difference and kinetic energy.

The electric potential difference, measured in volts (V), represents the amount of electric potential energy per unit charge available to move a charged particle between two points. The equation for electric potential difference is:

𝑉 = 𝐸/𝑞

Where 𝑉 is the electric potential difference (in volts), 𝐸 is the electric potential energy (in joules), and 𝑞 is the charge (in coulombs).

Since the electron has a negative charge of -1.6 x 10^(-19) coulombs, we can rearrange the equation to find the electric potential energy:

𝐸 = 𝑉 × 𝑞

Substituting the given values, we have:

𝐸 = 9V × (-1.6 x 10^(-19) C)

Calculating this expression will give us the electric potential energy gained by the electron.

𝐸 = -1.44 x 10^(-18) J

However, electric potential energy is transformed into kinetic energy as the electron moves between the terminals. We know that kinetic energy (𝐾) is given by the equation:

𝐾 = 1/2 × 𝑚 × 𝑣^2

Where 𝑚 is the mass of the electron (9.11 x 10^(-31) kg in this case) and 𝑣 is the velocity of the electron.

Since we are only concerned with the kinetic energy gained, we can ignore initial kinetic energy and assume the electron starts from rest (initial velocity = 0 m/s). Therefore, the equation simplifies to:

𝐾 = 1/2 × 𝑚 × (final velocity)^2

Now, we can directly relate the electric potential energy to the kinetic energy:

𝐾 = |𝐸|

Since the electron moves from the negative to the positive terminal (opposite to the direction of the electric field), the absolute value of the electric potential energy is taken.

Substituting the value of 𝐸 we calculated earlier:

𝐾 = |-1.44 x 10^(-18) J|

Calculating this expression will give us the kinetic energy gained by the electron as it moves from the negative terminal to the positive terminal of the battery.

𝐾 ≈ 1.44 x 10^(-18) J