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For a helium ion (He+) in its third Bohr orbit, using the non-relativistic model, what is the electron’s speed? Take K = 9 × 10⁹ kg m²/C², Z = 2, and Planck’s constant h = 6.6 × 10⁻³⁴ J s.

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

Orbital speed v_n = (Z/n)*2.18x10^6 m/s. For He+ with Z = 2, n = 3: v = (2/3)*2.18x10^6 ~ 1.46x10^6 m/s.

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