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An electron moves with a speed of 2.0 x 10\(^6\)ms\(^{-1}\) in a straight line. Calculate...

Physics
WAEC 2010

An electron moves with a speed of 2.0 x 10\(^6\)ms\(^{-1}\) in a straight line. Calculate the wavelength of the electron wave. [mass of an electron = 9.1 x 10\(^{-31}\) kg][Planck's constant = 6.6 x 10\(^{-34}\)Js]

  • A. 3.63 x 10-10m
  • B. 6.51 x 10-9m
  • C. 4.24 x 10-8m
  • D. 7.25 x 10-8m
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Correct Answer: Option A
Explanation

\(\lambda = \frac{\text{h}}{\text{mv}}\)
mv = 9.1 \(\times 10^{-31} \times 2.0 \times 10^6 = 1.82 \times 10^{-24} \, \text{kg m/s}\)
\(\lambda = \frac{6.6 \times 10^{-34}}{1.82 \times 10^{-24}} = 3.63 \times 10^{-10} \, \text{m}\)
3.63 × 10\(^{-10}\)


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