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What is the angular momentum of electron of Be³⁺ ion in n=5 orbit?

Asked in GSEB Board March 2023 · Bohr's rules in other systems

• (1) 3.3×10⁻³⁴ J s
• (2) 6.6×10⁻³⁴ J s
• (3) 5.3×10⁻³⁴ J s
• (4) 1.3×10⁻³⁴ J s

Step-by-step solution

Why the other options are wrong

• (1) comes from no single slip produces 3.3×10⁻³⁴ J s; it equals h/2, which leaves out both the n and the π of (nh)/(2π). Sanity check: (5h)/(2π)=5.3×10⁻³⁴ J s.
• (2) 6.6×10⁻³⁴ J s is Planck's constant itself; it drops the whole factor n/(2π) from L=(nh)/(2π).
• (4) 1.3×10⁻³⁴ J s divides (5h)/(2π) by Z=4, as if angular momentum shrank with nuclear charge the way the radius does; Bohr's condition has no Z in it.

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