A ball of mass 200g was thrown with the velocity of 20m/s. The de Broglie wavelength is:

Options

A. `3xx10^(-23)m`
B. `1.6xx10^(-34)m`
C. `3.6xx10^(-31)m`
D. `2.9xx10^(-33)m`

Explanation

To find the de Broglie wavelength of a ball with a mass of 200 g thrown at a velocity of 20 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. We need to convert this to kilograms since the standard unit of mass in physics is kilograms (kg).
\[ \text{Mass} (m) = 200 \text{ g} = 200 \times 10^{-3} \text{ kg} = 0.2 \text{ kg} \]

2. **Identify the Velocity:**
The velocity of the ball is given as:
\[ \text{Velocity} (v) = 20 \text{ m/s} \]

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

4. **Substitute the Values:**
Now, we can substitute the values of \(h\), \(m\), and \(v\) into the formula:
\[ \lambda = \frac{6.626 \times 10^{-34} \text{ J s}}{0.2 \text{ kg} \times 20 \text{ m/s}} \]

5. **Calculate the Denominator:**
First, calculate the denominator:
\[ 0.2 \text{ kg} \times 20 \text{ m/s} = 4 \text{ kg m/s} \]

6. **Calculate the Wavelength:**
Now, substitute this back into the equation for \(\lambda\):
\[ \lambda = \frac{6.626 \times 10^{-34}}{4} \]
\[ \lambda = 1.6565 \times 10^{-34} \text{ m} \]

7. **Final Result:**
Rounding it to two significant figures, we get:
\[ \lambda \approx 1.6 \times 10^{-34} \text{ m} \]

### Conclusion:
The de Broglie wavelength of the ball is approximately \(1.6 \times 10^{-34} \text{ m}\).

---