The wavelength associated with a ball of mass 100g moving with a speed of `10^(3) cm sec^(-1) (h=6.6 xx 10^(-34)Js)` is:

Options

A. `6.6 xx 10^(32) cm`
B. `6.6 xx 10^(-27) cm`
C. `6.6 xx 10^(27) cm`
D. `6.6 xx 10^(-32) cm`

Answer

To find the wavelength associated with a ball of mass 100 g moving with a speed of \(10^{3}\) cm/s, we can use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant (\(6.6 \times 10^{-34} \, \text{Js}\)),
- \(p\) is the momentum of the object, given by \(p = mv\) (mass times velocity).

### Step 1: Convert mass and velocity to SI units
1. **Convert mass from grams to kilograms:**
\[ m = 100 \, \text{g} = 100 \times 10^{-3} \, \text{kg} = 0.1 \, \text{kg} \]

2. **Convert velocity from cm/s to m/s:**
\[ v = 10^{3} \, \text{cm/s} = 10^{3} \times 10^{-2} \, \text{m/s} = 10 \, \text{m/s} \]

### Step 2: Calculate momentum
Using the formula for momentum:
\[ p = mv = 0.1 \, \text{kg} \times 10 \, \text{m/s} = 1 \, \text{kg m/s} \]

### Step 3: Calculate the wavelength using the de Broglie equation
Substituting the values into the de Broglie wavelength formula:
\[ \lambda = \frac{h}{p} = \frac{6.6 \times 10^{-34} \, \text{Js}}{1 \, \text{kg m/s}} = 6.6 \times 10^{-34} \, \text{m} \]

### Step 4: Convert wavelength from meters to centimeters
Since the question asks for the wavelength in centimeters:
\[ \lambda = 6.6 \times 10^{-34} \, \text{m} \times 100 \, \text{cm/m} = 6.6 \times 10^{-32} \, \text{cm} \]

### Final Answer
The wavelength associated with the ball is:
\[ \lambda = 6.6 \times 10^{-32} \, \text{cm} \]