A 0.66 kg ball is moving with a speed of 100 m/s. Find its wavelength

The correct option is 1.0 × 10⁻³⁵ m.

To find the wavelength of the moving ball, we use the de Broglie wavelength formula, which relates the wavelength of a particle to its momentum:
$$\lambda =\frac{h}{p}=\frac{h}{mv}$$

where:
• $\lambda$ is the de Broglie wavelength,
• $h$ is Planck's constant, approximately equal to $6.6\times {10}^{-34}\text{kg·m²/s}$ (or J·s),
• $m$ is the mass of the ball = 0.66 kg,
• $v$ is the velocity (speed) of the ball = 100 m/s.

First, let's calculate the momentum ($p$) of the ball:
$$p=m\times v=0.66\text{kg}\times 100\text{m/s}=66\text{kg·m/s}$$

Now, substitute the values of Planck's constant and the momentum into the de Broglie equation to calculate the wavelength:
$$\lambda =\frac{6.6\times {10}^{-34}}{66}$$

We can rewrite the denominator to make division straightforward:
$66=6.6\times {10}^1$

Substituting this back into the equation gives:
$$\lambda =\frac{6.6\times {10}^{-34}}{6.6\times {10}^1}=1.0\times {10}^{-34-1}=1.0\times {10}^{-35}\text{m}$$

Thus, the de Broglie wavelength of the ball is $1.0\times {10}^{-35}\text{m}$.