wavelength of Bullet. Calculate the de-Brogli wavelength of a 5.00 g bullet that is moving at 340 m/s will it exhibite wave like particle?

Explanation

To calculate the de Broglie wavelength of a bullet, we can follow these steps:

### Step 1: Understand the Formula
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{p} \]
where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \))
- \( p \) is the momentum of the object.

### Step 2: Calculate the Momentum
Momentum (p) is calculated using the formula:
\[ p = m \cdot v \]
where:
- \( m \) is the mass of the bullet in kilograms
- \( v \) is the velocity of the bullet in meters per second.

Given:
- Mass of the bullet = 5.00 g = \( 5.00 \times 10^{-3} \, \text{kg} \)
- Velocity of the bullet = 340 m/s

Now, substituting the values:
\[ p = (5.00 \times 10^{-3} \, \text{kg}) \cdot (340 \, \text{m/s}) = 1.70 \, \text{kg m/s} \]

### Step 3: Substitute Values into the De Broglie Formula
Now we can substitute the values of \( h \) and \( p \) into the de Broglie wavelength formula:
\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{1.70 \, \text{kg m/s}} \]

### Step 4: Calculate the Wavelength
Now performing the calculation:
\[ \lambda = \frac{6.626 \times 10^{-34}}{1.70} \approx 3.89 \times 10^{-34} \, \text{m} \]

### Step 5: Conclusion
The calculated de Broglie wavelength of the bullet is approximately \( 3.89 \times 10^{-34} \, \text{m} \).

Since this wavelength is extremely small, we can conclude that the bullet will not exhibit wave-like behavior as a particle. Wave-like properties are typically observable in microscopic particles like electrons, not in macroscopic objects like bullets.

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