To calculate the velocity and momentum of an electron given its kinetic energy, we need to use the equation for kinetic energy:
KE = (1/2)mv²,
where KE is the kinetic energy, m is the mass of the electron, and v is its velocity.
The mass of an electron is approximately 9.10938356 × 10^-31 kilograms.
Given that the kinetic energy is 100 electron volts (eV), we need to convert it to joules since the SI unit of energy is joules.
1 eV = 1.602176634 × 10^-19 joules.
So, the kinetic energy in joules is:
KE = 100 eV × (1.602176634 × 10^-19 J/eV) ≈ 1.602176634 × 10^-17 J.
Now, we can rearrange the kinetic energy equation to solve for velocity:
v = sqrt((2KE) / m).
Substituting the values:
v = sqrt((2 × 1.602176634 × 10^-17 J) / (9.10938356 × 10^-31 kg)).
Calculating this expression yields:
v ≈ 1.5855 × 10^6 meters per second.
To find the momentum, we can use the equation:
p = mv,
where p is the momentum.
Substituting the values:
p = (9.10938356 × 10^-31 kg) × (1.5855 × 10^6 m/s).
Calculating this expression gives:
p ≈ 1.446 × 10^-24 kilogram meters per second.
Therefore, for an electron with a kinetic energy of 100 eV, the velocity is approximately 1.5855 × 10^6 m/s, and the momentum is approximately 1.446 × 10^-24 kg·m/s.