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
1.35 ×10-15s
2.69 × 10-15s
4.15 × 10-15s
9.05 × 10-15s
1.62 × 10-14s
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This question tests your knowledge of Heisenberg's Uncertainty Principle.
However, the examiner set a massive psychological trap for you right in the middle of the sentence (The Useless Mass):
They gave you the mass of the electron 10^-³⁰kg
Do not use it! It is a complete decoy. Examiners love throwing in extra numbers to make you panic and try to force a kinetic energy formula where it doesn't belong. When dealing with the uncertainty of Energy and Time, mass is 100% irrelevant.
The Formula (The O'Level Shortcut):In advanced university physics, the full formula is $\Delta E \times \Delta t \ge \frac{h}{4\pi}$. But at the WAEC/NECO/JAMB level, the syllabus allows you to use the simplified approximation:$$\Delta E \times \Delta t \approx h$$Where:$\Delta E$ = Uncertainty in Energy = $2.45 \times 10^{-19} \text{ J}$$\Delta t$ = Uncertainty in Time = ? (This is what we want)$h$ = Planck's constant = $6.6 \times 10^{-34} \text{ J s}$Let's plug the numbers into our simplified formula:$$2.45 \times 10^{-19} \times \Delta t = 6.6 \times 10^{-34}$$Now, divide both sides to solve for $\Delta t$:$$\Delta t = \frac{6.6 \times 10^{-34}}{2.45 \times 10^{-19}}$$When you punch that into your calculator:$$\Delta t = 2.6938... \times 10^{-15}$$Rounding it off to two decimal places gives you exactly $2.69 \times 10^{-15} \text{ s}$!
from the question above, since energy was already given, mass isn't needed again. if you finish solving you'll realize that 1.35×10^-15 sec is the right answer. so Option A is the best answer. myschool pls correct this
