Question

The ionization potential of hydrogen atom is 13.6 ev . Calculate the speed of electron which could just ionized the hydrogen atom

Answer 1

ionisation potential of hydrogen atom, I.P = 13.6 volts

so, ionisation energy , I.E = charge on electron × I.P

= 13.6 eV

= 13.6 × 1.6 × 10^-19 Joule

= 2.176 × 10^-18 Joule

as you know, ionisation energy is amount of energy required to remove an electron from an isolated gaseous atom.

Let speed of electron = v which could just ionized the hydrogen atom.

so, kinetic energy = ionisation energy

or, 1/2 mv² = 2.176 × 10^-18

or, 1/2 × 9.1 × 10^-31 × v² = 2.176 × 10^-18 [ mass of electron is 9.1 × 10^-31 kg ]

or, 4.55 v² = 2.176 × 10¹³

or, v² = (21.76/4.55) × 10¹²

or, v² = 4.78 × 10¹²

or, v = 2.18 × 10^6 m/s

hence, speed of electron is 2.18 × 10^6 m/s