What is the de-Broglie wavelength of a 3 kg object moving with a speed of `2 ms^(-1)` ?

Options

A. `1.1xx 10^(-34)m`
B. `2.2xx 10^(-32)m`
C. `3.3xx 10^(-30)m`
D. `4.4xx 10^(-34)m`

Answer

To find the de-Broglie wavelength of a 3 kg object moving with a speed of 2 m/s, we can follow these steps:

### Step 1: Identify the given values
- Mass (m) = 3 kg
- Speed (v) = 2 m/s

### Step 2: Calculate the momentum (p)
The momentum (p) of an object is given by the formula:
\[ p = m \times v \]

Substituting the values:
\[ p = 3 \, \text{kg} \times 2 \, \text{m/s} = 6 \, \text{kg m/s} \]

### Step 3: Use the de-Broglie wavelength formula
The de-Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant, approximately \( 6.63 \times 10^{-34} \, \text{Js} \).

### Step 4: Substitute the values into the de-Broglie wavelength formula
Now we can substitute the values of \( h \) and \( p \):
\[ \lambda = \frac{6.63 \times 10^{-34} \, \text{Js}}{6 \, \text{kg m/s}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \lambda = 1.105 \times 10^{-34} \, \text{m} \]
(approximately \( 1.1 \times 10^{-34} \, \text{m} \))

### Final Answer
The de-Broglie wavelength of the object is approximately:
\[ \lambda \approx 1.1 \times 10^{-34} \, \text{m} \]

---