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

Options

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

Answer

To find the associated wavelength of a moving ball using De Broglie's equation, we can follow these steps:

### Step 1: Understand De Broglie's Equation
De Broglie's equation relates the wavelength (λ) of a particle to its momentum. The equation is given by:
\[ \lambda = \frac{h}{mv} \]
where:
- \( \lambda \) is the wavelength,
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( m \) is the mass of the particle in kilograms,
- \( v \) is the velocity of the particle in meters per second.

### Step 2: Identify the Given Values
From the question, we have:
- Mass of the ball, \( m = 0.66 \, \text{kg} \)
- Velocity of the ball, \( v = 100 \, \text{m/s} \)

### Step 3: Substitute the Values into the Equation
Now, we can substitute the values of \( h \), \( m \), and \( v \) into the De Broglie's equation:
\[ \lambda = \frac{6.626 \times 10^{-34}}{0.66 \times 100} \]

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

### Step 5: Calculate the Wavelength
Now substitute the value of \( mv \) back into the equation:
\[ \lambda = \frac{6.626 \times 10^{-34}}{66} \]

### Step 6: Perform the Division
Now perform the division:
\[ \lambda = 1.0039 \times 10^{-35} \, \text{m} \]

### Step 7: Final Result
Thus, the associated wavelength of the ball is approximately:
\[ \lambda \approx 1.0 \times 10^{-35} \, \text{m} \]

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

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