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: Convert the mass from grams to kilograms
The mass of the ball is given as 120 g. To convert this to kilograms, we use the conversion factor \(1 \text{ g} = 10^{-3} \text{ kg}\).

\[ \text{Mass (m)} = 120 \text{ g} = 120 \times 10^{-3} \text{ kg} = 0.120 \text{ kg} \]

### Step 2: Identify the velocity
The velocity of the ball is given as \(20 \text{ m/s}\).

\[ \text{Velocity (v)} = 20 \text{ m/s} \]

### Step 3: Use the de Broglie wavelength formula
The de Broglie wavelength (\(\lambda\)) is given by the formula:

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

where \(p\) is the momentum. The momentum (\(p\)) can be calculated as:

\[ p = mv \]

Substituting the values of mass and velocity:

\[ p = (0.120 \text{ kg}) \times (20 \text{ m/s}) = 2.4 \text{ kg m/s} \]

### Step 4: Substitute the values into the de Broglie wavelength formula
We know Planck's constant \(h = 6.6 \times 10^{-34} \text{ Js}\). Now we can substitute \(h\) and \(p\) into the de Broglie wavelength formula:

\[ \lambda = \frac{h}{p} = \frac{6.6 \times 10^{-34} \text{ Js}}{2.4 \text{ kg m/s}} \]

### Step 5: Calculate the wavelength
Now we perform the calculation:

\[ \lambda = \frac{6.6 \times 10^{-34}}{2.4} = 2.75 \times 10^{-34} \text{ m} \]

### Step 6: Express the answer in scientific notation
To express \(2.75 \times 10^{-34}\) in standard scientific notation, we can round it to two significant figures:

\[ \lambda \approx 2.8 \times 10^{-34} \text{ m} \]

### Final Answer
The de Broglie wavelength of the ball is approximately:

\[ \lambda \approx 2.8 \times 10^{-34} \text{ m} \]