A `0.66` kg ball is moving with a speed of 100 m/s. The associated wavelength will be `(h=6.6xx10^(-34)" J s")`

Options

A. `6.6xx10^(-32)` m
B. `6.6xx10^(-34)` m
C. `1.0xx10^(-35)` m
D. `1.0xx10^(-32)` m

Explanation

To find the associated wavelength of a moving ball, we can use the de Broglie wavelength formula, which is given by:

\[ \lambda = \frac{h}{mv} \]

where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant,
- \(m\) is the mass of the object,
- \(v\) is the velocity of the object.

### Step-by-Step Solution:

1. **Identify the given values**:
- Mass of the ball, \(m = 0.66 \, \text{kg}\)
- Velocity of the ball, \(v = 100 \, \text{m/s}\)
- Planck's constant, \(h = 6.6 \times 10^{-34} \, \text{J s}\)

2. **Calculate the linear momentum**:
- The linear momentum \(p\) is given by the formula:
\[ p = mv \]
Substituting the values:
\[ p = 0.66 \, \text{kg} \times 100 \, \text{m/s} = 66 \, \text{kg m/s} \]

3. **Substitute the values into the wavelength formula**:
- Now, substitute \(h\) and \(p\) into the wavelength formula:
\[ \lambda = \frac{h}{p} = \frac{h}{mv} \]
\[ \lambda = \frac{6.6 \times 10^{-34} \, \text{J s}}{66 \, \text{kg m/s}} \]

4. **Perform the calculation**:
- Calculate the wavelength:
\[ \lambda = \frac{6.6 \times 10^{-34}}{66} \approx 1.0 \times 10^{-35} \, \text{m} \]

5. **Final result**:
- The associated wavelength of the ball is approximately:
\[ \lambda \approx 1.0 \times 10^{-35} \, \text{m} \]

### Summary:
The associated wavelength of a 0.66 kg ball moving at 100 m/s is \(1.0 \times 10^{-35} \, \text{m}\).