A `0.66 kg` ball is moving wih a speed of `100 m//s`. The associated wavelength will be.

Options

A. `6.6 xx 10^-32 m`
B. `6.6 xx 10^-34 m`
C. `1.0 xx 10^-35 m`
D. `1.0 xx 10^-32 m`

Explanation

To find the associated wavelength of a moving ball using the De Broglie wavelength formula, follow these steps:

### Step 1: Write down the De Broglie wavelength formula
The De Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( h \) is the Planck's constant (\( 6.63 \times 10^{-34} \, \text{Js} \)),
- \( m \) is the mass of the object (in kg),
- \( v \) is the velocity of the object (in m/s).

### Step 2: Identify the values
From the problem:
- Mass \( m = 0.66 \, \text{kg} \)
- Velocity \( v = 100 \, \text{m/s} \)

### Step 3: Substitute the values into the formula
Substituting the known values into the De Broglie wavelength formula:
\[ \lambda = \frac{6.63 \times 10^{-34} \, \text{Js}}{(0.66 \, \text{kg}) \times (100 \, \text{m/s})} \]

### Step 4: Calculate the denominator
Calculate the product of mass and velocity:
\[ mv = 0.66 \, \text{kg} \times 100 \, \text{m/s} = 66 \, \text{kg m/s} \]

### Step 5: Calculate the wavelength
Now substitute the calculated value of \( mv \) back into the equation:
\[ \lambda = \frac{6.63 \times 10^{-34} \, \text{Js}}{66 \, \text{kg m/s}} \]

### Step 6: Perform the division
Calculating the value:
\[ \lambda = 1.003 \times 10^{-35} \, \text{m} \]

### Step 7: Final result
The associated wavelength of the ball is approximately:
\[ \lambda \approx 1.003 \times 10^{-35} \, \text{m} \]