Read Perturbed Bohr Orbits: Expand About the Usual Radius
A small extra central force changes the Bohr radius only slightly. Keep angular-momentum quantisation exact and solve the force balance to first order in the small length δ.
Perturbed Bohr Orbits is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
Discard terms containing δ times that correction.
Build the governing relation
The correction must have dimensions of length and must disappear as δ tends to zero. That immediately rules out changes that scale as n δ without the right dimensions.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Substituting the unperturbed radius everywhere misses the first-order shift; retain the linear correction before dropping second-order terms.
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