The de-Broglie wavelength of a tennis ball mass ` 60 g` moving with a velocity of ` 10 m` per second is approximately :

Options

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

Answer

To calculate 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 (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(m\) is the mass of the object in kilograms,
- \(v\) is the velocity of the object in meters per second.

### Step 1: Convert the mass from grams to kilograms
The mass of the tennis ball is given as \(60 \, \text{g}\). We need to convert this to kilograms:

\[ m = 60 \, \text{g} = 60 \times 10^{-3} \, \text{kg} = 0.060 \, \text{kg} \]

### Step 2: Identify the velocity
The velocity of the tennis ball is given as:

\[ v = 10 \, \text{m/s} \]

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

\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{(0.060 \, \text{kg})(10 \, \text{m/s})} \]

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

\[ mv = (0.060 \, \text{kg})(10 \, \text{m/s}) = 0.6 \, \text{kg m/s} \]

### Step 5: Calculate the de-Broglie wavelength
Now, substituting the denominator back into the formula:

\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{0.6 \, \text{kg m/s}} = 1.10433 \times 10^{-33} \, \text{m} \]

### Step 6: Round the result
Rounding the result to three significant figures, we get:

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

### Final Answer
The de-Broglie wavelength of the tennis ball is approximately \(1.105 \times 10^{-33} \, \text{m}\).

---