Final answer:
To calculate the electron's velocity in a hydrogen atom, one can use the ionization energy of 13.6 eV and equate this to the electron's kinetic energy, and then solve for velocity.
Step-by-step explanation:
The energy of 13.6 eV is required to ionize a hydrogen atom, which corresponds to the energy needed to separate a hydrogen atom into a proton and an electron. To find the velocity of the electron in the hydrogen atom, we must apply the conservation of energy principle. The kinetic energy (KE) of the electron can be equated to the energy required to remove it from the atom. Since KE for an electron can be expressed as (1/2)mv², where 'm' is the mass of the electron and 'v' is its velocity, we can solve for 'v' using the given ionization energy of 13.6 eV.
To convert electron volts to joules (the SI unit of energy), we use the conversion factor 1 eV = 1.602 x 10⁻¹⁹ J. The mass of an electron is approximately 9.109 x 10⁻³¹ kg. Therefore, we can determine the velocity 'v' by solving the equation 13.6 eV × (1.602 x 10⁻¹⁹ J/eV) = (1/2) × (9.109 x 10⁻³¹ kg) × v², leading to the velocity's numerical value.