Answer :
The de Broglie wavelength of a 148 g baseball thrown at 38.1 m/s is calculated using the formula λ = h / mv, resulting in the wavelength 2.06 × 10-35 , demonstrating the theory's relevance primarily to particles much smaller than a baseball.
The question asks to calculate the de Broglie wavelength of a baseball with a mass of 148 g (0.148 kg) thrown at a velocity of 38.1 meters per second. To find the wavelength, we use the formula λ = h / mv, where 'h' is Planck's constant (6.62607015 × 10-34 m2 kg / s), 'm' is the mass of the baseball, and 'v' is its velocity. Substituting the values into the equation, we calculate the de Broglie wavelength.
Calculation:
λ = h / mv,
λ = 6.62607015 × 10-34 / (0.148 kg × 38.1 m/s)
= 1.16 × 10-34 m2kg / (5.63 kg m/s)
= 1.16 × 10-34 / 5.63
= 2.06 × 10-35 meters.
This calculated wavelength is extremely small, reflecting how de Broglie wavelengths become significant primarily for particles with very small mass and/or high velocities. The de Broglie wavelength of a 148 g baseball thrown at 38.1 m/s is 2.06 × 10-35 meters.
