At what speed must a 145-g baseball travel to have a wavelength of 1.15 × 10⁻³⁴ m?

• A. 39.7 m/s
• B. 3.97 × 10² m/s
• C. 1.80 × 10⁴³ m/s
• D. 3.98 × 10⁹ m/s
• E. 18 m/s

Answer: (A)

Verified step by step guidance

1. Identify the concept involved: This problem involves the de Broglie wavelength, which relates the wavelength of a particle to its momentum. The de Broglie wavelength formula is: λ = h / (m * v), where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 Js), m is the mass of the particle, and v is the velocity of the particle.
2. Convert the mass of the baseball from grams to kilograms, since the standard unit of mass in physics is kilograms. The mass of the baseball is 145 g, which is equivalent to 0.145 kg.
3. Rearrange the de Broglie wavelength formula to solve for velocity (v): v = h / (m * λ).
4. Substitute the known values into the rearranged formula: Planck's constant (h) is 6.626 x 10^-34 Js, the mass (m) is 0.145 kg, and the wavelength (λ) is 1.15 x 10^-34 m.
5. Calculate the velocity (v) using the substituted values to find the speed at which the baseball must travel to have the given wavelength.