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Consider 3rd orbit of He⁺ (Helium), using non-relativistic approach, the speed of electron in this orbit will be [given K = 9 × 10⁹ constant, Z = 2 and h (Planck's Constant) = 6.6 × 10⁻³⁴ Js]:

1. 1.46 × 10⁶ m/s
2. 0.73 × 10⁶ m/s
3. 3.0 × 10⁸ m/s
4. 2.92 × 10⁶ m/s

Correct answer: 1.46 × 10⁶ m/s

Solution

The speed of an electron in the nth orbit of a hydrogen-like atom is given by v = (Z * e²) / (2 * ε₀ * h * n), where Z is the atomic number, n is the orbit number, and constants are substituted. For He⁺ (Z = 2) in the 3rd orbit (n = 3), substituting values gives v ≈ 1.46 × 10⁶ m/s.

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