An electron of mass 9.1 x 10 ^ -31 kg moves with a speed of 2.0 x 10 ^6 ms ^ -1 round the nucleus of an atom…

Analyze the question: We need the centripetal force on an electron moving in a circle. The formula is F = mv²/r.

Given:

• m = 9.1 × 10⁻³¹ kg
• v = 2.0 × 10⁶ m/s
• r = 6.1 × 10¹¹ m (as printed)

Calculation with the radius as printed:

v² = 4.0 × 10¹² m²/s²

mv² = 9.1 × 10⁻³¹ × 4.0 × 10¹² = 3.64 × 10⁻¹⁸

F = 3.64 × 10⁻¹⁸ / 6.1 × 10¹¹ ≈ 6.0 × 10⁻³⁰ N

This matches none of the options. The radius of an atom's orbit cannot be 10¹¹ m, since that is larger than the Earth. The original question almost certainly has r = 6.1 × 10⁻¹¹ m, and the minus sign was lost in the formatting.

Calculation with r = 6.1 × 10⁻¹¹ m:

F = 3.64 × 10⁻¹⁸ / 6.1 × 10⁻¹¹

F ≈ 0.597 × 10⁻⁷ ≈ 6.0 × 10⁻⁸ N

Note: With the radius exactly as typed (10¹¹), the answer would be about 6.0 × 10⁻³⁰ N, which is not listed. So the question as pasted has a typo, and the intended radius is 6.1 × 10⁻¹¹ m. Check your question paper to confirm.

Tip: Always check that the powers of ten make physical sense. Atomic radii are around 10⁻¹⁰ m, so a positive exponent signals a typo. Also, write F = mv²/r and combine the powers of ten separately from the numbers to avoid slips.