According to the de Broglie equation, the wavelength ($\lambda$) associated with a material particle of mass $m$ moving with velocity $v$ is given by: $\lambda = \frac{h}{mv}$

Given: Mass, $m = 0.66 \text{ kg}$ Velocity, $v = 100 \text{ m/s}$

• Planck's constant, $h = 6.6 \times 10^{-34} \text{ Js}$ (Note: The standard value is $6.626 \times 10^{-34}$, but the question specifies $6.6$).

Calculation: $\lambda = \frac{6.6 \times 10^{-34} \text{ kg m}^2\text{s}^{-1}}{0.66 \text{ kg} \times 100 \text{ m s}^{-1}}$ $\lambda = \frac{6.6 \times 10^{-34}}{66}$ $\lambda = 0.1 \times 10^{-34} \text{ m}$ $\lambda = 1.0 \times 10^{-35} \text{ m}$

This problem illustrates that for macroscopic objects (like a ball), the de Broglie wavelength is extremely small and not observable, consistent with the discussion in the NCERT text .