Discussion
The kinetic energy of a fast-moving particle of mass 1 x 10-31kg is associated with a de Broglie wavelength 63nm is (h = 6.3 x 10-34 Js)
Answer: C
The kinetic energy is 5 x 10-22 J.
From \(\lambda = \frac{h}{mv}\) and \(K = \frac{1}{2}mv^{2}\), \(K = \frac{h^{2}}{2m\lambda^{2}}\).
\[ \begin{aligned} v &= \frac{6.3 \times 10^{-34}}{10^{-31} \times 63 \times 10^{-9}} \\ &= 10^{5}\ \text{m s}^{-1} \\ K &= \tfrac{1}{2} \times 10^{-31} \times (10^{5})^{2} \\ &= 5 \times 10^{-22}\ \text{J} \end{aligned} \]
The option \(1 \times 10^{-21}\) J forgets the \(\frac{1}{2}\) in kinetic energy, and \(5 \times 10^{-21}\) J slips a power of ten.
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