Practice portal › Atoms › Bohr Model of the Hydrogen Atom

13.6 eV energy is required to separate a hydrogen atom into a proton and an electron. Compute the orbital radius of the corresponding electron.

Asked in GSEB Board March 2020 · Postulates, radius, speed and angular momentum

• (1) 5.3×10⁻¹¹ m
• (2) 10.6×10⁻¹¹ m
• (3) 2.65×10⁻¹¹ m
• (4) 1.33×10⁻¹¹ m

Step-by-step solution

Why the other options are wrong

• (2) 10.6×10⁻¹¹ m comes from setting 13.6 eV equal to the size of the potential energy, (ke²)/r, forgetting that the kinetic energy gives back half of it; the binding energy is (ke²)/(2r).
• (3) comes from no single slip produces 2.65×10⁻¹¹ m, which is half the true radius. Sanity check: r=(ke²)/(2E) with these values gives 5.3×10⁻¹¹ m.
• (4) comes from no single slip produces 1.33×10⁻¹¹ m, a quarter of the true radius. Sanity check: r=(ke²)/(2E)=5.3×10⁻¹¹ m, the familiar Bohr radius.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.