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:

\[ \lambda = \frac{H}{P} = \frac{H}{MV} \]

Where:
- \(\lambda\) is the wavelength,
- \(H\) is the Planck constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(M\) is the mass of the object,
- \(V\) is the velocity of the object.

### Step-by-Step Solution:

**Step 1: Convert the mass of the fighter jet from tons to kilograms.**
- Given mass = 2 tons.
- Since \(1 \, \text{ton} = 1000 \, \text{kg}\), we have:
\[ M = 2 \, \text{tons} = 2 \times 1000 \, \text{kg} = 2000 \, \text{kg} \]

**Step 2: Identify the velocity of the fighter jet.**
- Given velocity \(V = 1500 \, \text{m/s}\).

**Step 3: Substitute the values into the De Broglie wavelength formula.**
- We know:
\[ H = 6.626 \times 10^{-34} \, \text{Js} \]
- Now substitute \(H\), \(M\), and \(V\) into the formula:
\[ \lambda = \frac{H}{MV} = \frac{6.626 \times 10^{-34}}{2000 \times 1500} \]

**Step 4: Calculate the denominator.**
- Calculate \(MV\):
\[ MV = 2000 \, \text{kg} \times 1500 \, \text{m/s} = 3000000 \, \text{kg m/s} \]

**Step 5: Calculate the wavelength.**
- Now substitute back into the equation:
\[ \lambda = \frac{6.626 \times 10^{-34}}{3000000} \]
- Performing the division:
\[ \lambda = 2.20866667 \times 10^{-40} \, \text{m} \]
- Rounding to three significant figures:
\[ \lambda \approx 2.209 \times 10^{-40} \, \text{m} \]

### Final Answer:
The wavelength of a 2-ton fighter jet aircraft flying with a velocity of 1500 m/s is approximately \(2.209 \times 10^{-40} \, \text{m}\).