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Which one of the following represents Bohr's radius?

Asked in GSEB Board July 2022 · Postulates, radius, speed and angular momentum

• (1) (ε₀²h²)/(4π me²)
• (2) (ε₀h)/(2π me²)
• (3) (4πε₀h²)/(me²)
• (4) (ε₀h²)/(π me²)

Step-by-step solution

Why the other options are wrong

• (1) comes from no single slip produces this, and a dimension check rules it out: (ε₀h²)/(me²) is a length, so the extra factor ε₀ leaves this expression with dimensions [M⁻¹L⁻²T⁴A²], not those of a length.
• (2) comes from no single slip produces this; it has one power of h too few. (ε₀h²)/(me²) is a length, so dividing out an h leaves [M⁻¹L⁻¹T], not a length.
• (3) comes from this is the textbook form a₀=(4πε₀ℏ²)/(me²) with h written where ℏ=h/(2π) belongs, which makes it 4π² times too large (about 2.1×10⁻⁹ m).

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