The de-Broglie wavelength of the tennis ball of mass 60g moving with a velocity of `10m//s` is approx.: (Plank's constant `h=6.63xx10^(-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 with a mass of 60 g moving at a velocity of 10 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 (\(6.63 \times 10^{-34} \, \text{Js}\)),
- \(m\) is the mass of the object in kg,
- \(v\) is the velocity of the object in m/s.

### Step 1: Convert the mass from grams to kilograms
The mass of the tennis ball is given as 60 g. To convert grams to kilograms:

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

### Step 2: Use the given velocity
The velocity of the tennis ball is given as 10 m/s, which is already in SI units.

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

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

\[ \lambda = \frac{6.63 \times 10^{-34} \, \text{Js}}{(0.060 \, \text{kg})(10 \, \text{m/s})} \]

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

\[ mv = (0.060 \, \text{kg})(10 \, \text{m/s}) = 0.60 \, \text{kg m/s} \]

### Step 5: Calculate the de-Broglie wavelength
Now substitute the value of \(mv\) back into the equation:

\[ \lambda = \frac{6.63 \times 10^{-34} \, \text{Js}}{0.60 \, \text{kg m/s}} = 1.105 \times 10^{-33} \, \text{m} \]

### Step 6: Round the result
For simplicity, we can round this to:

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

### Conclusion
Thus, the de-Broglie wavelength of the tennis ball is approximately:

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