Question

Calculate the de Broglie wavelength of a 0.075 kg softball thrown at a velocity of 15 m/s.

a) 1.125 x 10^-34 m
b) 5.625 x 10^-36 m
c) 2.5 x 10^-35 m
d) 1.5 x 10^-35 m

Answer 1

To find the de Broglie wavelength of the softball, the de Broglie equation is used, but the calculated result does not exactly match any of the given options, concluding that all options are incorrect.

Step-by-step explanation:

To calculate the de Broglie wavelength of a 0.075 kg softball thrown at a velocity of 15 m/s, we use the de Broglie equation \( \lambda = \frac{h}{mv} \), where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) J·s), \( m \) is the mass of the softball, and \( v \) is the velocity.

Substituting the given values into the equation, we get:

\( \lambda = \frac{6.626 \times 10^{-34} \text{ J·s}}{0.075 \text{ kg} \times 15 \text{ m/s}} \)

\( \lambda = \frac{6.626 \times 10^{-34}}{1.125} \)

\( \lambda = 5.89 \times 10^{-35} \text{ m} \)

Looking at the given options, none match the calculated result exactly. Therefore, we conclude that none of the given options (a) 1.125 x 10^-34 m, (b) 5.625 x 10^-36 m, (c) 2.5 x 10^-35 m, (d) 1.5 x 10^-35 m, is correct.