To calculate the kinetic energy (KE) and linear momentum (p) of a moving electron given its rest mass and the ratio of its moving mass to its rest mass, we can use the relativistic formulas. The relativistic kinetic energy formula is:
KE = (γ - 1) * mc²
where γ (gamma) is the Lorentz factor given by γ = 1 / sqrt(1 - v²/c²), m is the rest mass of the electron, and c is the speed of light.
The linear momentum (p) of the electron can be calculated using the relativistic momentum formula:
p = γ * mv
where γ (gamma) is the same Lorentz factor, m is the rest mass of the electron, and v is the velocity of the electron.
Let's substitute the given information into these formulas:
Given: Mass of moving electron (m') = 11 * Rest mass of electron (m)
Since the ratio of the moving mass to the rest mass is given as 11, we can write:
m' = 11m
Since the rest mass of an electron is approximately 9.11 × 10^(-31) kilograms, we have:
m' = 11 * 9.11 × 10^(-31) kg
Now, we can calculate the kinetic energy and linear momentum.
First, let's find the rest mass of the electron (m):
m = 9.11 × 10^(-31) kg
Next, let's calculate the moving mass of the electron (m'):
m' = 11 * m = 11 * 9.11 × 10^(-31) kg
Now, we can calculate the Lorentz factor (γ):
γ = 1 / sqrt(1 - v²/c²)
Since the velocity (v) is not given, we cannot determine the Lorentz factor, kinetic energy, and linear momentum without additional information.