A 200 g cricket ball is thrown with a speed of `3 xx 10^3` cm/sec, what will be its de-Broglie wavelength?

Options

A. `1.1 xx 10^(-32)cm`
B. `2.2 xx 10^(-32)cm`
C. `0.55 xx 10^(-32)cm`
D. `11.0 xx 10^(-32)cm`

Answer

To find the de-Broglie wavelength of a cricket ball, we can use the de-Broglie wavelength formula:

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

where:
- \(\lambda\) is the de-Broglie wavelength,
- \(h\) is the Planck constant,
- \(m\) is the mass of the object,
- \(v\) is the velocity of the object.

### Step-by-Step Solution:

**Step 1: Convert the mass of the cricket ball to grams.**
- Given mass of the cricket ball = 200 g (no conversion needed since it's already in grams).

**Step 2: Convert the speed from cm/sec to the appropriate units.**
- Given speed = \(3 \times 10^3\) cm/sec (no conversion needed since it's already in cm/sec).

**Step 3: Identify the value of Planck's constant.**
- Planck's constant \(h = 6.6 \times 10^{-27}\) g cm²/sec.

**Step 4: Substitute the values into the de-Broglie wavelength formula.**
\[ \lambda = \frac{h}{mv} = \frac{6.6 \times 10^{-27}}{200 \times (3 \times 10^3)} \]

**Step 5: Calculate the denominator.**
- Calculate \(200 \times (3 \times 10^3)\):
\[ 200 \times 3 \times 10^3 = 600 \times 10^3 = 6 \times 10^5 \text{ g cm/sec} \]

**Step 6: Substitute the denominator back into the formula.**
\[ \lambda = \frac{6.6 \times 10^{-27}}{6 \times 10^5} \]

**Step 7: Perform the division.**
\[ \lambda = 1.1 \times 10^{-32} \text{ cm} \]

**Step 8: Write the final answer.**
- The de-Broglie wavelength of the cricket ball is \(1.1 \times 10^{-32}\) cm.

### Final Answer:
\(\lambda = 1.1 \times 10^{-32} \text{ cm}\)