What is the uncertainty in the measurement of time, if the uncertainty in measuring the energy of an electron of mass 10-30 kg is 2.45 × 10-19J? h = 6.6 × 10-34

Analyze the question: This is the Heisenberg uncertainty principle for energy and time: ΔE·Δt ≥ h/(4π). The mass of the electron is extra information and isn't needed.

Concept: The usual textbook form is ΔE·Δt ≈ h/(2π) or h/(4π), depending on the syllabus. We need to see which one matches an option.

Solution:

Using Δt = h/(4π ΔE):

• h = 6.6 × 10⁻³⁴ J·s
• 4π = 12.566
• 4π × ΔE = 12.566 × 2.45 × 10⁻¹⁹ = 3.079 × 10⁻¹⁸
• Δt = 6.6 × 10⁻³⁴ / 3.079 × 10⁻¹⁸ = 2.14 × 10⁻¹⁶ s

This matches none of the options.

Using Δt = h/(2π ΔE):

• 2π = 6.283
• 2π × ΔE = 6.283 × 2.45 × 10⁻¹⁹ = 1.539 × 10⁻¹⁸
• Δt = 6.6 × 10⁻³⁴ / 1.539 × 10⁻¹⁸ = 4.29 × 10⁻¹⁶ s

This also matches none of the options.

Using Δt = h/ΔE:

• Δt = 6.6 × 10⁻³⁴ / 2.45 × 10⁻¹⁹ = 2.69 × 10⁻¹⁵ s

This matches option B.

So the question uses the simplified form ΔE·Δt ≈ h, which gives 2.69 × 10⁻¹⁵ s.

With the more standard forms (h/4π or h/2π), the answer would be about 10⁻¹⁶ s, which is not among the options. The question evidently intends the simple approximation ΔE·Δt = h, so B is the only option that fits.

Exam tip: When the options don't match the h/4π or h/2π results, try ΔE·Δt = h. Also remember that the mass is a distractor here, since it is not needed for the energy-time relation. Always check the order of magnitude (10⁻³⁴ / 10⁻¹⁹ = 10⁻¹⁵) to quickly spot the right option.