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

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

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

### Step 1: Convert mass from grams to kilograms
The mass of the ball is given as 100g. We need to convert this into kilograms:

\[ m = 100 \, \text{g} = \frac{100}{1000} \, \text{kg} = 0.1 \, \text{kg} \]

### Step 2: Convert velocity from cm/s to m/s
The velocity is given as \(10^3 \, \text{cm/s}\). We need to convert this into meters per second:

\[ v = 10^3 \, \text{cm/s} = 10^3 \times \frac{1}{100} \, \text{m/s} = 10^1 \, \text{m/s} = 10 \, \text{m/s} \]

### 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:

\[ \lambda = \frac{h}{mv} = \frac{6.626 \times 10^{-34} \, \text{Js}}{(0.1 \, \text{kg})(10 \, \text{m/s})} \]

### Step 4: Calculate the wavelength
Now we perform the calculation:

\[ \lambda = \frac{6.626 \times 10^{-34}}{1} = 6.626 \times 10^{-34} \, \text{m} \]

### Final Answer
The wavelength associated with the ball is:

\[ \lambda = 6.626 \times 10^{-34} \, \text{m} \]