Calculate De Broglie wavelength of bullet moving with speed 90m/sec and having a mass 5 gm.

Answer

To calculate the de Broglie wavelength of a bullet moving with a speed of 90 m/s and having a mass of 5 grams, 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 (\( 6.63 \times 10^{-34} \, \text{Js} \)),
- \( m \) is the mass of the object in kilograms,
- \( v \) is the velocity of the object in meters per second.

### Step 2: Convert Mass to Kilograms
The mass of the bullet is given as 5 grams. To use the formula, we need to convert this into kilograms:
\[ m = 5 \, \text{grams} = 5 \times 10^{-3} \, \text{kg} \]

### Step 3: Substitute Values into the Formula
Now we can substitute the values into the de Broglie wavelength formula:
\[ \lambda = \frac{6.63 \times 10^{-34} \, \text{Js}}{(5 \times 10^{-3} \, \text{kg}) \times (90 \, \text{m/s})} \]

### Step 4: Calculate the Denominator
First, calculate the denominator:
\[ m \cdot v = (5 \times 10^{-3} \, \text{kg}) \times (90 \, \text{m/s}) = 4.5 \times 10^{-1} \, \text{kg m/s} \]

### Step 5: Calculate the Wavelength
Now substitute the value of the denominator back into the formula:
\[ \lambda = \frac{6.63 \times 10^{-34}}{4.5 \times 10^{-1}} \]
Calculating this gives:
\[ \lambda = 1.47 \times 10^{-33} \, \text{m} \]

### Final Result
Thus, the de Broglie wavelength of the bullet is:
\[ \lambda \approx 1.47 \times 10^{-33} \, \text{meters} \]