Question

A $0.66\, kg$ ball is moving with a speed of $100 \,m/s$. The associated wavelength will be $(h = 6.6 \times 10^{-34} \, Js)$

• A. $ 6.6 \times 10^{-34} m $
• B. $ 1.0 \times 10^{-35} m $
• C. $ 1.0\times 10^{-32} m $
• D. $ 6.6 \times 10^{-32} m $

Answer 1

The Correct Option is B

To solve this problem, we need to determine the wavelength of a macroscopic object, specifically a ball. We can use the de Broglie wavelength formula, which describes the wave nature of particles:

\(\lambda = \frac{h}{mv}\)

where:

• \(\lambda\) is the wavelength,
• h = 6.6 \times 10^{-34} \, Js\) is the Planck's constant,
• m = 0.66 \, kg\) is the mass of the ball,
• v = 100 \, m/s\) is the velocity of the ball.

Let's substitute these values into the formula:

\(\lambda = \frac{6.6 \times 10^{-34} \, Js}{0.66 \, kg \times 100 \, m/s}\)

Simplifying this expression:

\(\lambda = \frac{6.6 \times 10^{-34}}{66}\)

\(\lambda = 1 \times 10^{-35} \, m\)

Thus, the associated wavelength of the ball is 1 \times 10^{-35} \, m.

Conclusion: The correct answer is 1.0 \times 10^{-35} \, m.

This reasoning matches the given correct option. For macroscopic objects like this ball, the de Broglie wavelength is extremely small and typically undetectable, highlighting the quantum mechanical behavior that is negligible at macroscopic scales.