Calculate the wavelength of a tennis ball of mass 60 gm moving with a velocity of 10 m per second. `(h=6.626 xx 10^(-34) kg m^(2) s^(-1))`

Answer

To calculate the wavelength of a tennis ball of mass 60 grams moving with a velocity of 10 m/s, we will use the de Broglie wavelength formula:

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

Where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{kg m}^2/\text{s}\)),
- \(m\) is the mass of the object in kilograms,
- \(v\) is the velocity of the object in meters per second.

### Step 1: Convert mass from grams to kilograms
The mass of the tennis ball is given as 60 grams. To convert grams to kilograms, we use the conversion factor \(1 \, \text{kg} = 1000 \, \text{g}\).

\[ m = 60 \, \text{g} \times \frac{1 \, \text{kg}}{1000 \, \text{g}} = 0.06 \, \text{kg} \]

### Step 2: Identify the velocity
The velocity of the tennis ball is given as \(10 \, \text{m/s}\).

### 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:

\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{kg m}^2/\text{s}}{0.06 \, \text{kg} \times 10 \, \text{m/s}} \]

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

\[ mv = 0.06 \, \text{kg} \times 10 \, \text{m/s} = 0.6 \, \text{kg m/s} \]

### Step 5: Calculate the wavelength
Now substitute the value of \(mv\) back into the formula:

\[ \lambda = \frac{6.626 \times 10^{-34}}{0.6} \]

Calculating this gives:

\[ \lambda \approx 1.10433 \times 10^{-33} \, \text{m} \]

### Step 6: Final result
We can express this in scientific notation:

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

Thus, the wavelength of the tennis ball is approximately \(1.1 \times 10^{-33} \, \text{m}\).

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