A body of mass 70 kg travels with a speed of 15 km/hour. Calculate the de-Broglie wavelength of the body.

Answer

To calculate the de-Broglie wavelength of a body with a mass of 70 kg traveling at a speed of 15 km/hour, we will follow these steps:

### Step 1: Understand the formula for de-Broglie wavelength
The formula for de-Broglie wavelength (λ) is given by:
\[ \lambda = \frac{h}{mv} \]
where:
- \( \lambda \) = de-Broglie wavelength
- \( h \) = Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\))
- \( m \) = mass of the body (in kg)
- \( v \) = speed of the body (in m/s)

### Step 2: Convert speed from km/hour to m/s
The speed given is 15 km/hour. To convert this to meters per second (m/s), we use the conversion factor:
\[ 1 \, \text{km} = 1000 \, \text{m} \quad \text{and} \quad 1 \, \text{hour} = 3600 \, \text{seconds} \]
Thus, the conversion is:
\[ v = 15 \, \text{km/hour} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{hour}}{3600 \, \text{s}} = \frac{15000}{3600} \approx 4.17 \, \text{m/s} \]

### Step 3: Substitute the values into the formula
Now we have:
- \( h = 6.626 \times 10^{-34} \, \text{Js} \)
- \( m = 70 \, \text{kg} \)
- \( v \approx 4.17 \, \text{m/s} \)

Substituting these values into the de-Broglie wavelength formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{70 \times 4.17} \]

### Step 4: Calculate the denominator
Calculating the denominator:
\[ 70 \times 4.17 \approx 291.9 \]

### Step 5: Calculate the de-Broglie wavelength
Now substituting back into the equation:
\[ \lambda = \frac{6.626 \times 10^{-34}}{291.9} \approx 2.27 \times 10^{-36} \, \text{m} \]

### Final Result
The de-Broglie wavelength of the body is approximately:
\[ \lambda \approx 2.27 \times 10^{-36} \, \text{meters} \]

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