The wavelength associated with a golf ball weighing 200 g and moving at a speed of `"5 m h"^(-1)` is of the order:

Options

A. `10^(-10)m`
B. `10^(-20)m`
C. `10^(-30)m`
D. `10^(-40)m`

Explanation

To find the wavelength associated with a golf ball weighing 200 g and moving at a speed of 5 m/h, we will use the de Broglie wavelength formula:

### Step-by-Step Solution:

1. **Identify the Formula**:
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( h \) = Planck's constant = \( 6.626 \times 10^{-34} \, \text{Js} \)
- \( m \) = mass of the object in kg
- \( v \) = velocity of the object in m/s

2. **Convert Mass**:
The mass of the golf ball is given as 200 g. We need to convert this to kilograms:
\[ m = 200 \, \text{g} = 0.2 \, \text{kg} \]

3. **Convert Velocity**:
The speed of the golf ball is given as 5 m/h. We need to convert this to meters per second:
\[ v = 5 \, \text{m/h} = \frac{5}{3600} \, \text{m/s} \approx 1.39 \times 10^{-3} \, \text{m/s} \]

4. **Substitute Values into the Formula**:
Now, substitute the values of \( h \), \( m \), and \( v \) into the de Broglie wavelength formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{0.2 \times 1.39 \times 10^{-3}} \]

5. **Calculate the Denominator**:
First, calculate \( 0.2 \times 1.39 \times 10^{-3} \):
\[ 0.2 \times 1.39 \times 10^{-3} = 0.000278 \, \text{kg m/s} \]

6. **Calculate the Wavelength**:
Now, calculate \( \lambda \):
\[ \lambda = \frac{6.626 \times 10^{-34}}{0.000278} \approx 2.38 \times 10^{-30} \, \text{m} \]

7. **Express in Scientific Notation**:
The wavelength can be expressed in scientific notation:
\[ \lambda \approx 2.38 \times 10^{-30} \, \text{m} \]

### Conclusion:
The wavelength associated with the golf ball is of the order of \( 10^{-30} \, \text{m} \).