To find the speed of a particle given its mass and wavelength, we can use the de Broglie wavelength formula, which relates the wavelength of a particle to its momentum. The formula is: \[ \lambda = \frac{h}{p} \] where: - \(\lambda\) is the wavelength, - \(h\) is Planck's constant (\(6.63 \times 10^{-34} \, \text{Js}\)), - \(p\) is the momentum of the particle. Momentum (\(p\)) can also be expressed in terms of mass (\(m\)) and velocity (\(v\)): \[ p = mv \] By substituting this expression for momentum into the de Broglie equation, we get: \[ \lambda = \frac{h}{mv} \] Rearranging this equation to solve for velocity (\(v\)), we have: \[ v = \frac{h}{m\lambda} \] ### Step-by-Step Calculation 1. **Identify the given values**: - Mass (\(m\)) = \(10^{-27} \, \text{kg}\) - Wavelength (\(\lambda\)) = \(10^{-8} \, \text{m}\) - Planck's constant (\(h\)) = \(6.63 \times 10^{-34} \, \text{Js}\) 2. **Substitute the values into the velocity formula**: \[ v = \frac{6.63 \times 10^{-34} \, \text{Js}}{(10^{-27} \, \text{kg})(10^{-8} \, \text{m})} \] 3. **Calculate the denominator**: \[ (10^{-27} \, \text{kg})(10^{-8} \, \text{m}) = 10^{-35} \, \text{kg m} \] 4. **Now substitute back into the equation**: \[ v = \frac{6.63 \times 10^{-34}}{10^{-35}} = 6.63 \times 10^{1} \, \text{m/s} = 66.3 \, \text{m/s} \] ### Conclusion The speed of the particle is \(66.3 \, \text{m/s}\), which corresponds to option **B**. ### Explanation of Other Options - **Option A: 6.63 m/s**: This value is too low. It likely results from a misunderstanding of the units or a miscalculation in the application of the de Broglie formula. - **Option C: 663.00 m/s**: This value is too high. It may arise from an incorrect calculation, possibly by misapplying the formula or misinterpreting the values of mass and wavelength. - **Option D: 6630.00 m/s**: This value is significantly higher than expected. It suggests a major error in the calculation, such as misplacing the decimal point or misunderstanding the relationship between mass, wavelength, and speed. ### Revision Summary - Use the de Broglie wavelength formula: \(\lambda = \frac{h}{mv}\) to relate wavelength, mass, and speed. - Rearrange to find speed: \(v = \frac{h}{m\lambda}\). - Substitute known values carefully and perform calculations step-by-step to avoid errors. - Always check the units and ensure they are consistent throughout the calculation.