The de - Broglie wavelength of a ball of mass 120 g moving at a speed of `"20 m s"^(-1)` is (Planck's constant `h=6.6xx10^(-34)Js`)

Options

A. `3.5xx10^(-34)m`
B. `2.8xx10^(-34)m`
C. `1.2xx10^(-34)m`
D. `2.1xx10^(-34)m`

Answer

To find the de Broglie wavelength of a ball of mass 120 g moving at a speed of 20 m/s, we can follow these steps:

### Step 1: Write the formula for de Broglie wavelength
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the object.

### Step 2: Express momentum in terms of mass and velocity
The momentum \( p \) can be expressed as:
\[ p = m \cdot v \]
where \( m \) is the mass of the object and \( v \) is its velocity.

### Step 3: Convert mass from grams to kilograms
Given the mass of the ball is 120 g, we need to convert this to kilograms:
\[ m = 120 \, \text{g} = 120 \times 10^{-3} \, \text{kg} = 0.120 \, \text{kg} \]

### Step 4: Substitute values into the momentum formula
Now, substituting the values into the momentum formula:
\[ p = 0.120 \, \text{kg} \cdot 20 \, \text{m/s} = 2.4 \, \text{kg m/s} \]

### Step 5: Substitute the values into the de Broglie wavelength formula
Now we can substitute \( h \) and \( p \) into the de Broglie wavelength formula:
\[ \lambda = \frac{6.6 \times 10^{-34} \, \text{Js}}{2.4 \, \text{kg m/s}} \]

### Step 6: Calculate the de Broglie wavelength
Calculating the above expression:
\[ \lambda = \frac{6.6 \times 10^{-34}}{2.4} = 2.75 \times 10^{-34} \, \text{m} \]

### Step 7: Round the result
We can round this to:
\[ \lambda \approx 2.8 \times 10^{-34} \, \text{m} \]

### Conclusion
Thus, the de Broglie wavelength of the ball is approximately \( 2.8 \times 10^{-34} \, \text{m} \).