What will be the wavelength of a 2 ton fighter jet aircraft flying with a velocity of `1500 msec^(-1)` ?

Options

A. `1.112 xx 10^(-38)m`
B. `2.208 xx 10^(-40)m`
C. `7.889 xx 10^(-27)m`
D. `1.576 xx 10^(-34) m`

Explanation

To find the wavelength of a 2-ton fighter jet aircraft flying with a velocity of 1500 m/s, we will use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(m\) is the mass of the object,
- \(v\) is the velocity of the object.

### Step 1: Convert the mass from tons to kilograms
Since 1 ton is equal to 1000 kg, we convert 2 tons to kilograms:
\[ m = 2 \, \text{tons} = 2 \times 1000 \, \text{kg} = 2000 \, \text{kg} \]

### Step 2: Write down the values
Now we have:
- \(h = 6.626 \times 10^{-34} \, \text{Js}\)
- \(m = 2000 \, \text{kg}\)
- \(v = 1500 \, \text{m/s}\)

### Step 3: Substitute the values into the de Broglie wavelength formula
Now we can substitute the values into the formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{2000 \times 1500} \]

### Step 4: Calculate the denominator
First, calculate the denominator:
\[ 2000 \times 1500 = 3000000 \, \text{kg m/s} \]

### Step 5: Calculate the wavelength
Now substitute the denominator back into the equation:
\[ \lambda = \frac{6.626 \times 10^{-34}}{3000000} \]
\[ \lambda = \frac{6.626 \times 10^{-34}}{3 \times 10^{6}} = 2.20867 \times 10^{-40} \, \text{m} \]

### Step 6: Round the answer
Rounding to three significant figures, we get:
\[ \lambda \approx 2.21 \times 10^{-40} \, \text{m} \]

### Final Answer
The wavelength of the 2-ton fighter jet aircraft flying at a velocity of 1500 m/s is approximately:
\[ \lambda \approx 2.21 \times 10^{-40} \, \text{m} \]

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