Calculate the wavelength of 1000 kg rocket moving with a velocity of 3000 km/hr. `(h=6.626 xx 10^(-34) kg m^(2)s^(-1))`

Answer

To calculate the wavelength of a rocket moving with a certain velocity, we can use the de Broglie wavelength formula:

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

Where:
- \(\lambda\) = wavelength
- \(h\) = Planck's constant (\(6.626 \times 10^{-34} \, \text{kg m}^2/\text{s}\))
- \(m\) = mass of the object (in kg)
- \(v\) = velocity of the object (in m/s)

### Step 1: Convert the velocity from km/hr to m/s
The velocity is given as \(3000 \, \text{km/hr}\). We need to convert this to meters per second (m/s).

\[ 1 \, \text{km} = 1000 \, \text{m} \]
\[ 1 \, \text{hour} = 3600 \, \text{seconds} \]

To convert km/hr to m/s, we use the conversion factor:

\[ \text{Velocity in m/s} = \text{Velocity in km/hr} \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = \text{Velocity in km/hr} \times \frac{1}{3.6} \]

Calculating:

\[ v = 3000 \, \text{km/hr} \times \frac{1}{3.6} = 833.33 \, \text{m/s} \]

### Step 2: Substitute values into the de Broglie wavelength formula
Now that we have the mass \(m = 1000 \, \text{kg}\) and the velocity \(v = 833.33 \, \text{m/s}\), we can substitute these values into the formula.

\[ \lambda = \frac{h}{mv} = \frac{6.626 \times 10^{-34} \, \text{kg m}^2/\text{s}}{1000 \, \text{kg} \times 833.33 \, \text{m/s}} \]

### Step 3: Calculate the denominator
Calculating the denominator:

\[ 1000 \, \text{kg} \times 833.33 \, \text{m/s} = 833330 \, \text{kg m/s} \]

### Step 4: Calculate the wavelength
Now substituting back into the equation:

\[ \lambda = \frac{6.626 \times 10^{-34}}{833330} \]

Calculating:

\[ \lambda = 7.95 \times 10^{-40} \, \text{m} \]

### Final Answer
The wavelength of the rocket is:

\[ \lambda \approx 7.95 \times 10^{-40} \, \text{m} \]