Calculate the de Broglie wavelength associated with a ²⁰Ne⁺ ion moving at a velocity of 2.0 × 10⁵ m/s. The atomic mass of Ne-20 is 19.992 amu. (1 amu = 1.66 × 10^-24 g and h = 6.63 × 10^-34 J • s) A) 1.0 × 10^-13 m B) 1.0 × 10^-16 m C) 1.0 × 10^-18 m D) 9.7 × 10¹² m E) 2.0 × 10^-13 cm

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Quizplus · Accepted Answer

The de Broglie wavelength ($\lambda$) is given by the formula $\lambda = \frac{h}{mv}$, where $h$ is Planck's constant, $m$ is the mass in kg, and $v$ is the velocity in m/s. First, convert the mass of the Ne-20 ion from amu to kg: $19.992 \, \text{amu} \times 1.66 \times 10^{-27} \, \text{kg/amu} = 3.32 \times 10^{-26} \, \text{kg}$. Then, calculate the wavelength: $\lambda = \frac{6.63 \times 10^{-34}}{3.32 \times 10^{-26} \times 2.0 \times 10^{5}} = 1.0 \times 10^{-13} \, \text{m}$.

Calculate the De Broglie Wavelength Associated with a 20Ne+ Ion

Calculate the De Broglie Wavelength Associated with a ²⁰Ne⁺ Ion