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AIIMS 2010
Exam
AIIMS
Year
2010
Subject
Chemistry
Chapter
Structure of Atom

AIIMS 2010 · Chemistry · Structure of Atom

Assume that you are travelling at a speed of 90 ~km / h in a small...

Assume that you are travelling at a speed of 90 km/h90 \mathrm{~km} / \mathrm{h} in a small car with a mass of 1050 kg1050 \mathrm{~kg}. If the uncertainty in the velocity of the car is 1%(Δv=0.9 km/h)1 \%(\Delta v=0.9 \mathrm{~km} / \mathrm{h}), what is the uncertainty (in meters) in the position of the car ?

Options

  1. AΔx≥1×10−35 m\Delta x \geq 1 \times 10^{-35} \mathrm{~m}
  2. BΔx≥2×10−37 m\Delta x \geq 2 \times 10^{-37} \mathrm{~m}
  3. CΔx≥2×10−36 m\Delta x \geq 2 \times 10^{-36} \mathrm{~m}
  4. DΔx≥4×10−38 m\Delta x \geq 4 \times 10^{-38} \mathrm{~m}

Correct answer

B. Δx≥2×10−37 m\Delta x \geq 2 \times 10^{-37} \mathrm{~m}

Step-by-step solution

\Deltax≥h(4π)(mΔv)\Deltax≥6.626×10−34(4×3.14×1050)(0.9)(13600)(10001)\Deltax≥2×10−37 m\begin{aligned}& \Deltax \geq \frac{h}{(4 \pi)(m \Delta v)}\\ & \Deltax \geq \frac{6.626 \times 10^{-34}}{(4 \times 3.14 \times 1050)(0.9)\left(\frac{1}{3600}\right)\left(\frac{1000}{1}\right)}\\ & \Deltax \geq 2 \times10^{-37} \mathrm{~m} \end{aligned}The uncertainty in the position of the car is far smaller than the uncertainty in the position of an electron in a hydrogen atom (3×10−10 m)\left(3 \times 10^{-10} \mathrm{~m}\right) and far too small a value to have any measurable consequences.
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