A cricket ball of 0.5 kg is moving with a velocity of `100ms^(-1)`. The wavelength associated with its motion is :

Options

A. `1//100cm`
B. `65xx10^(-34)m`
C. `1.32xx10^(-35)m`
D. `6.6xx10^(-28)m`

Explanation

To find the wavelength associated with the motion of a cricket ball using the de Broglie wavelength formula, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Mass of the cricket ball (m) = 0.5 kg
- Velocity of the cricket ball (v) = 100 m/s
- Planck's constant (h) = \(6.626 \times 10^{-34}\) Joule·s

2. **Write the de Broglie Wavelength Formula**:
The de Broglie wavelength (\(\lambda\)) is given by the formula:
\[ \lambda = \frac{h}{mv} \]

3. **Substitute the Values into the Formula**:
Substitute the values of \(h\), \(m\), and \(v\) into the formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{0.5 \times 100} \]

4. **Calculate the Denominator**:
First, calculate the product of mass and velocity:
\[ mv = 0.5 \times 100 = 50 \text{ kg·m/s} \]

5. **Calculate the Wavelength**:
Now, substitute this value back into the equation for \(\lambda\):
\[ \lambda = \frac{6.626 \times 10^{-34}}{50} \]
\[ \lambda = 1.3252 \times 10^{-35} \text{ meters} \]

6. **Round the Answer**:
Rounding the answer to two decimal places gives:
\[ \lambda \approx 1.32 \times 10^{-35} \text{ meters} \]

### Final Answer:
The wavelength associated with the motion of the cricket ball is approximately \(1.32 \times 10^{-35}\) meters.

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