13.6 eV energy is required to separate a hydrogen atom into proton and an electron. If the orbital radius of an electron in hydrogen atom is 5.3 × 10⁻¹¹ m, then velocity of electron is .

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(4) 2.2 × 10⁶ ms⁻¹. Given: 13.6 eV is needed to pull the atom apart, so the electron is bound with total energy E=-13.6 eV; its orbital radius is r=5.3×10⁻¹¹ m. Idea: the Coulomb attraction of the proton supplies the centripetal force, (mv²)/r=(ke²)/(r²), which gives v=√(ke²)/(mr). v=√(9×10⁹×(1.6×10⁻¹⁹)²)/(9.1×10⁻³¹×5.3×10⁻¹¹)=√4.78×10¹² m s⁻¹. v=2.19×10⁶ m s⁻¹≈2.2×10⁶ m s⁻¹. The energy route agrees, which is why the 13.6 eV is given: K=-E=13.6 eV, so v=√(2K)/m=√(2×13.6×1.6×10⁻¹⁹)/(9.1×10⁻³¹)=2.2×10⁶ m s⁻¹.

13.6 eV energy is required to separate a hydrogen atom into proton and an electron. If the orbital radius of an electron in hydrogen atom is 5.3 × 10⁻¹¹ m, then velocity of electron is ______.

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