Question

what is the de broglie wavelength (in meters) of a 58.1 g tennis ball when served at a velocity of 44.5 meters per second?

Answer 1

The de Broglie wavelength of a 58.1 g tennis ball served at a velocity of 44.5 m/s is approximately
`2.05 × 10^-34` meters.

Step-by-step explanation:

The de Broglie wavelength of an object is given by the equation λ = h/mv, where λ is the wavelength, h is Planck's constant (6.62607015 × 10^-34 m^2 kg / s), m is the mass of the object, and v is its velocity. To find the de Broglie wavelength of a 58.1 g tennis ball served at a velocity of 44.5 m/s, we need to first convert the mass to kilograms:

m = 58.1 g = 0.0581 kg

Now we can use the equation to calculate the wavelength:

λ = (6.62607015 × 10^-34 m^2 kg / s) / (0.0581 kg * 44.5 m/s)

λ ≈
`2.05 × 10^-34 meters`

Answer 2

The de Broglie wavelength of a 58.1 g tennis ball served at a velocity of 44.5 m/s is approximately 2.55 x 10^-34 meters, calculated using the de Broglie wavelength formula with Planck's constant, the mass of the ball in kilograms, and the given velocity.

Step-by-step explanation:

The de Broglie wavelength of an object can be calculated using the formula λ = h/mv, where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 m^2kg/s), m is the mass of the object, and v is the velocity of the object. For a 58.1 g tennis ball served at a velocity of 44.5 meters per second, the mass (m) needs to be converted to kilograms before we can perform our calculation.

First, convert mass from grams to kilograms: 58.1 g = 0.0581 kg.

Then, calculate the de Broglie wavelength (λ): λ = (6.626 x 10^-34 m2kg/s) / (0.0581 kg x 44.5 m/s).

After computing the above, we find that the de Broglie wavelength of the tennis ball is approximately 2.55 x 10^-34 meters.