The de-Broglie wavelength associated with a ball of mass 150 g traveling at 30.0 m/s would be

The correct option is 1.47 x 10⁻³⁴ m.

To find the de-Broglie wavelength associated with the ball, we use the de-Broglie relation:
$$\lambda =\frac{h}{p}=\frac{h}{mv}$$
where:
• $\lambda$ is the de-Broglie wavelength,
• $h$ is Planck's constant ($6.626\times {10}^{-34}\text{ J·s}$ or $\text{kg·}{\text{m}}^2\text{/s}$),
• $m$ is the mass of the object,
• $v$ is the velocity of the object.

Step 1: Convert the given values into SI units
Given mass of the ball, $m=150\text{ g}=150\times {10}^{-3}\text{ kg}=0.15\text{ kg}$.
Given velocity of the ball, $v=30.0\text{ m/s}$.

Step 2: Substitute the values into the formula
$$\lambda =\frac{6.626\times {10}^{-34}}{0.15\times 30.0}$$
First, calculate the momentum ($p=mv$) in the denominator:
$$mv=0.15\times 30.0=4.5\text{ kg·m/s}$$
Now, calculate the wavelength:
$$\lambda =\frac{6.626\times {10}^{-34}}{4.5}$$
$$\lambda \approx 1.472\times {10}^{-34}\text{ m}$$
Rounding to three significant figures, we get:
$$\lambda =1.47\times {10}^{-34}\text{ m}$$

Thus, the de-Broglie wavelength associated with the traveling ball is 1.47 x 10⁻³⁴ m.