To calculate the speed of an electron that can ionize a hydrogen atom, we can use the principle of conservation of energy. The energy required to ionize a hydrogen atom is equal to its ionization potential, which is given as 13.6 electron volts (eV).
First, we need to convert the ionization potential from electron volts to joules since we'll be using SI units for the calculation.
1 eV is equal to 1.602 x 10^-19 joules.
So, the ionization potential of hydrogen in joules would be:
13.6 eV × 1.602 x 10^-19 J/eV = 2.18 x 10^-18 J
The energy of a moving particle can be expressed as:
E = (1/2) mv^2
Where: E is the kinetic energy of the electron m is the mass of the electron v is the velocity of the electron
Since we know the energy required (ionization potential) and the mass of an electron, we can rearrange the equation to solve for velocity:
v = sqrt(2E / m)
Substituting the values:
v = sqrt(2 × 2.18 x 10^-18 J / (9.10938356 × 10^-31 kg)
v ≈ 2.18 x 10^6 m/s
Therefore, the speed of the electron required to ionize a hydrogen atom is approximately 2.18 x 10^6 meters per second.