A ball of mass 200g was thrown with the velocity of 50m/s. The de Broglie wavelength is:

Options

A. `6.6xx10^(-34)`m
B. `6.6xx10^(-35)`m
C. `6.6xx10^(-33)`m
D. All of these

Explanation

To find the de Broglie wavelength of a ball with a mass of 200 g thrown at a velocity of 50 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Mass to Kilograms**:
The mass of the ball is given as 200 grams. To convert grams to kilograms, we use the conversion factor:
\[ \text{mass in kg} = \text{mass in g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 200 \text{ g} \times 10^{-3} = 0.2 \text{ kg} \]

2. **Identify the Velocity**:
The velocity of the ball is given as:
\[ v = 50 \text{ m/s} \]

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

4. **Substitute the Values into the Formula**:
Now we substitute the values into the formula:
\[ \lambda = \frac{6.626 \times 10^{-34} \text{ Js}}{0.2 \text{ kg} \times 50 \text{ m/s}} \]

5. **Calculate the Denominator**:
First, calculate the denominator:
\[ 0.2 \text{ kg} \times 50 \text{ m/s} = 10 \text{ kg m/s} \]

6. **Calculate the Wavelength**:
Now substitute this back into the equation for \(\lambda\):
\[ \lambda = \frac{6.626 \times 10^{-34}}{10} = 6.626 \times 10^{-35} \text{ m} \]

7. **Final Result**:
Therefore, the de Broglie wavelength of the ball is:
\[ \lambda \approx 6.626 \times 10^{-35} \text{ m} \]