The Bohr radius increases in higher orbits because the electron __________.
moves farther away from the nucleus
According to Bohr's model of the atom, electrons revolve around the nucleus only in certain fixed, quantised circular orbits (stationary states) without radiating energy. Bohr derived an expression for the radius of the nth orbit by balancing the electrostatic force of attraction between the nucleus and the electron with the centripetal force needed for circular motion, combined with the quantisation of angular momentum (mvr = nh/2π).
The resulting formula for the radius of the nth orbit in a hydrogen-like atom is:
rn = n² × a₀ / Z (for hydrogen, Z = 1, so rn = n² × a₀)
where a₀ is the Bohr radius (the radius of the first/innermost orbit), equal to 0.529 Å, and n is the principal quantum number (n = 1, 2, 3… for successive orbits/shells).
Because rn is proportional to n², the orbit radius grows rapidly as n increases:
- n = 1 (ground state): r = 1² × a₀ = 0.529 Å
- n = 2: r = 2² × a₀ = 4a₀ = 2.116 Å
- n = 3: r = 3² × a₀ = 9a₀ = 4.761 Å
Physically, this happens because higher orbits correspond to a greater angular momentum (n is larger), and to sustain a stable circular orbit at that angular momentum around the same nuclear charge, the electron must occupy a larger radius — i.e., it moves progressively farther away from the nucleus. This also explains why electrons in higher shells are more loosely bound (their energy, En = −13.6/n² eV, becomes less negative, i.e., closer to zero, as n increases), since the electrostatic attraction weakens with increasing distance.
The other listed possibilities are not consistent with Bohr's theory: the electron's charge remains a fixed, unchanging −e in every orbit — it never becomes positively charged; the electron does not lose all of its kinetic energy in a higher orbit, it simply has a different (smaller) kinetic energy consistent with a larger orbit, since total energy is still negative (bound state) until n → ∞; and the electron continues to orbit in every stationary state — it does not stop moving, since Bohr's postulate requires continuous, non-radiating circular motion in each allowed orbit.
Similar Questions
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Important Questions from Structure of Atom
Identify the element having zero valency
The atomic number of an element is 8. How many electrons will it gain to form a compound with sodium?
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