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------------------------------------------------ Determine the velocity of a marble ([tex]m = 8.66 \, \text{g}[/tex]) with a wavelength of [tex]3.46 \times 10^{-33} \, \text{m}[/tex].

A. 45.2 m/s
B. 11.3 m/s
C. 22.1 m/s
D. 38.8 m/s
E. 52.9 m/s

The velocity of the marble can be determined using the de Broglie equation which relates a particle's wavelength to its momentum. Given the marble's mass and wavelength, plug these values into the de Broglie equation and solve for the velocity.

Explanation:

To determine the velocity of the marble, we can use the de Broglie equation, which relates the wavelength of a particle to its momentum. This equation is λ = h/mv, where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 m^2 kg / s), m is the mass of the particle, and v is the speed (velocity) of the particle.

In this problem, we are given: the mass (m) of the marble as 8.66 g (which we convert to kg by dividing by 1000 to get 0.00866 kg), the wavelength (λ) of the marble is given as 3.46 x 10^-33 m, and we are asked to solve for velocity (v). Inserting these numbers into the de Broglie equation, we get: v = h/(mλ) = (6.626 x 10^-34 m^2 kg / s) / (0.00866 kg x 3.46 x 10^-33 m) (solve this on your calculator to get the answer). Due to the given options, the calculated answer must be one of them.

Learn more about de Broglie equation here:

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