Physics Dawn of Modern Physics MDCAT 2018
PMDC Verified Question 45 of 52
The de Broglie wave length of an electron travelling with a speed of \( 1.0 \times 10^7 \text{ m/s} \) equal to, (\( h = 6.6 \times 10^{-34} \text{ Js} \) and \( m_e = 9.1 \times 10^{-31} \text{ kg} \)):
A
\( 7.3 \times 10^{11} \text{ m} \)
B
\( 7.3 \times 10^{-11} \text{ m} \)
C
\( 7.3 \times 10^{10} \text{ m} \)
D
\( 7.3 \times 10^{-10} \text{ m} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( 7.3 \times 10^{-11} \text{ m} \)
Concept:

Electrons exhibit wave-like properties; their wavelength is determined by their momentum.

Formula:

$$ \lambda = \frac{h}{mv} $$

Solution:

  • Substitute the specific values provided in the prompt: \( \lambda = \frac{6.6 \times 10^{-34}}{(9.1 \times 10^{-31}) \times (1.0 \times 10^7)} \).


  • \( \lambda = \frac{6.6 \times 10^{-34}}{9.1 \times 10^{-24}} \)


  • \( \lambda = 0.725 \times 10^{-10} \text{ m} \).


  • Adjusting to standard scientific notation: \( 7.25 \times 10^{-11} \text{ m} \), which rounds to \( 7.3 \times 10^{-11} \text{ m} \).


Why other options are incorrect:

Positive exponents imply a macroscopic, physically impossible wavelength for an electron. The \( 10^{-10} \) option stems from an error shifting the decimal point.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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