The de Broglie wavelength associated with a ball of mass 200 g and moving at a speed of 5 metres/hour, is of the order of (`h = 6.625xx10^(-34)`J s) is

Options

A. `10^(-15)`m
B. `10^(-20)`m
C. `10^(-25)`m
D. `10^(-30)`m

Explanation

To find the de Broglie wavelength associated with a ball of mass 200 g moving at a speed of 5 meters/hour, we can use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the de Broglie wavelength,
- \(h\) is the Planck constant (\(6.625 \times 10^{-34} \, \text{J s}\)),
- \(m\) is the mass of the object in kg,
- \(v\) is the velocity of the object in m/s.

### Step 1: Convert the mass from grams to kilograms
The mass of the ball is given as 200 g. To convert this to kilograms:

\[ m = \frac{200 \, \text{g}}{1000} = 0.2 \, \text{kg} \]

### Step 2: Convert the speed from meters/hour to meters/second
The speed of the ball is given as 5 meters/hour. To convert this to meters/second:

\[ v = \frac{5 \, \text{m/h}}{3600 \, \text{s/h}} = \frac{5}{3600} \, \text{m/s} \approx 0.00138889 \, \text{m/s} \]

### Step 3: Substitute the values into the de Broglie wavelength formula
Now we can substitute the values of \(h\), \(m\), and \(v\) into the de Broglie wavelength formula:

\[ \lambda = \frac{6.625 \times 10^{-34} \, \text{J s}}{(0.2 \, \text{kg}) \times (0.00138889 \, \text{m/s})} \]

### Step 4: Calculate the denominator
Calculating the denominator:

\[ 0.2 \, \text{kg} \times 0.00138889 \, \text{m/s} = 0.000277778 \, \text{kg m/s} \]

### Step 5: Calculate the wavelength
Now substituting back into the equation:

\[ \lambda = \frac{6.625 \times 10^{-34}}{0.000277778} \approx 2.39 \times 10^{-30} \, \text{m} \]

### Conclusion
The de Broglie wavelength associated with the ball is approximately \(2.39 \times 10^{-30} \, \text{m}\).

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