The velocity of a body of mass 10 gm is `2 xx 10^(4) ms^(-1)`. The value of de - Broglie waavelenght associated with it will be

Options

A. `3.3 xx 10^(-33) m`
B. `3.3 xx 10^(-34) m`
C. `3.3 xx 10^(-35) m`
D. `3.3 xx 10^(-36)m`

Explanation

To find the de Broglie wavelength associated with a body of mass 10 grams moving at a velocity of \(2 \times 10^4 \, \text{ms}^{-1}\), we can use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the de Broglie wavelength,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(p\) is the momentum of the particle, given by \(p = mv\) (mass times velocity).

### Step 1: Convert mass from grams to kilograms
The mass of the body is given as 10 grams. To convert grams to kilograms, we use the conversion factor \(1 \, \text{g} = 0.001 \, \text{kg}\):

\[ m = 10 \, \text{g} = 10 \times 10^{-3} \, \text{kg} = 0.01 \, \text{kg} \]

### Step 2: Calculate the momentum
Using the formula for momentum \(p = mv\), we can substitute the values for mass and velocity:

\[ v = 2 \times 10^4 \, \text{ms}^{-1} \]

Now, substituting the values:

\[ p = m \cdot v = (0.01 \, \text{kg}) \cdot (2 \times 10^4 \, \text{ms}^{-1}) = 0.01 \times 20000 = 200 \, \text{kg m/s} \]

### Step 3: Calculate the de Broglie wavelength
Now, we can substitute the values of \(h\) and \(p\) into the de Broglie wavelength formula:

\[ \lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34} \, \text{Js}}{200 \, \text{kg m/s}} \]

Calculating this gives:

\[ \lambda = \frac{6.626 \times 10^{-34}}{200} = 3.313 \times 10^{-36} \, \text{m} \]

### Final Answer
Thus, the value of the de Broglie wavelength associated with the body is:

\[ \lambda \approx 3.3 \times 10^{-36} \, \text{m} \]