The de-Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 m/s is approximately (Plank's constant `h=6.63 xx 10^(-34)Js)`

Options

A. `10^(-33)m`
B. `10^(-31)m`
C. `10^(-16)m`
D. `10^(-25)m`

Explanation

To find the de Broglie wavelength of a tennis ball, we can use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the de Broglie wavelength,
- \(h\) is Planck's constant,
- \(m\) is the mass of the object,
- \(v\) is the velocity of the object.

### Step 1: Convert the mass from grams to kilograms
The mass of the tennis ball is given as 60 g. We need to convert this to kilograms since the standard unit of mass in the SI system is kilograms.

\[ m = 60 \, \text{g} = \frac{60}{1000} \, \text{kg} = 0.06 \, \text{kg} \]

### Step 2: Write down the values
Now we have:
- \(h = 6.63 \times 10^{-34} \, \text{Js}\)
- \(m = 0.06 \, \text{kg}\)
- \(v = 10 \, \text{m/s}\)

### Step 3: Substitute the values into the de Broglie wavelength formula
Now we can substitute these values into the formula:

\[ \lambda = \frac{6.63 \times 10^{-34}}{0.06 \times 10} \]

### Step 4: Calculate the denominator
First, calculate the denominator:

\[ 0.06 \times 10 = 0.6 \]

### Step 5: Perform the division
Now we can perform the division:

\[ \lambda = \frac{6.63 \times 10^{-34}}{0.6} \]

Calculating this gives:

\[ \lambda = 1.105 \times 10^{-33} \, \text{m} \]

### Step 6: Round to the appropriate significant figures
Rounding this value to two significant figures gives approximately:

\[ \lambda \approx 1.1 \times 10^{-33} \, \text{m} \]

### Conclusion
Thus, the de Broglie wavelength of the tennis ball is approximately \(10^{-33} \, \text{m}\). Therefore, the correct answer is the first option.