Calculate the de-broglie wavelength associated with motion of earth `(mass6xx10^(24)kg)` orbiting around the sun at a speedof `3xx10^(6)m//s`.

Explanation

To calculate the de Broglie wavelength associated with the motion of the Earth orbiting around the Sun, we can follow these steps:

### Step 1: Understand the Formula
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( h \) is Planck's constant, approximately \( 6.626 \times 10^{-34} \, \text{Js} \)
- \( m \) is the mass of the object (in this case, the Earth)
- \( v \) is the velocity of the object

### Step 2: Identify Known Values
From the question, we have:
- Mass of the Earth, \( m = 6 \times 10^{24} \, \text{kg} \)
- Speed of the Earth, \( v = 3 \times 10^{6} \, \text{m/s} \)

### Step 3: Substitute Values into the Formula
Now we can substitute the known values into the de Broglie wavelength formula:
\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{(6 \times 10^{24} \, \text{kg}) \times (3 \times 10^{6} \, \text{m/s})} \]

### Step 4: Calculate the Denominator
First, calculate the denominator:
\[ m \cdot v = (6 \times 10^{24} \, \text{kg}) \times (3 \times 10^{6} \, \text{m/s}) = 18 \times 10^{30} \, \text{kg m/s} = 1.8 \times 10^{31} \, \text{kg m/s} \]

### Step 5: Calculate the Wavelength
Now substitute the denominator back into the equation:
\[ \lambda = \frac{6.626 \times 10^{-34}}{1.8 \times 10^{31}} \]
Calculating this gives:
\[ \lambda \approx 3.68 \times 10^{-65} \, \text{m} \]

### Final Answer
Thus, the de Broglie wavelength associated with the motion of the Earth orbiting around the Sun is approximately:
\[ \lambda \approx 3.68 \times 10^{-65} \, \text{m} \]

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