Calculate the de Broglie wavelength of a ball of mass 0.1 kg moving with a speed of `60ms^(-1)`.

Answer

To calculate the de Broglie wavelength of a ball with a mass of 0.1 kg moving at a speed of 60 m/s, we can use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the de Broglie wavelength,
- \(h\) 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 of the object (in m/s).

### Step-by-Step Solution:

1. **Identify the values:**
- Mass (\(m\)) = 0.1 kg
- Velocity (\(v\)) = 60 m/s
- Planck's constant (\(h\)) = \(6.626 \times 10^{-34} \, \text{Js}\)

2. **Substitute the values into the formula:**
\[ \lambda = \frac{6.626 \times 10^{-34}}{0.1 \times 60} \]

3. **Calculate the denominator:**
\[ 0.1 \times 60 = 6 \]

4. **Now substitute back into the equation:**
\[ \lambda = \frac{6.626 \times 10^{-34}}{6} \]

5. **Perform the division:**
\[ \lambda = 1.10433 \times 10^{-34} \, \text{m} \]

6. **Round to two significant figures:**
\[ \lambda \approx 1.1 \times 10^{-34} \, \text{m} \]

### Final Answer:
The de Broglie wavelength of the ball is approximately \(1.1 \times 10^{-34} \, \text{m}\).