The de Broglie wave length of a riffle bullet of mass 2 grams moving with a velocity of 2m/sec of

Options

A. `(6.6 xx 10^(-34))/(2 xx 2)m`
B. `(6.6 xx 10^(-27))/(2 xx 10^(-3) xx 2) cm`
C. `(6.6 xx 10^(-34))/(2 xx 10^(-3) xx 2) m`
D. `(6.6 xx 10^(-27))/(2 xx 2) m`

Answer

To find the de Broglie wavelength of a rifle bullet, we will use the de Broglie wavelength formula:

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

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

### Step 1: Convert the mass from grams to kilograms
Given mass = 2 grams.

To convert grams to kilograms:
\[ m = 2 \, \text{grams} = 2 \times 10^{-3} \, \text{kg} \]

### Step 2: Identify the velocity
Given velocity = 2 m/s.

### Step 3: Substitute the values into the de Broglie wavelength formula
Now we can substitute the values of \(h\), \(m\), and \(v\) into the formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{(2 \times 10^{-3}) \times (2)} \]

### Step 4: Calculate the denominator
Calculate the denominator:
\[ (2 \times 10^{-3}) \times (2) = 4 \times 10^{-3} \]

### Step 5: Substitute the denominator back into the formula
Now substitute the denominator back into the formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{4 \times 10^{-3}} \]

### Step 6: Perform the division
Now, perform the division:
\[ \lambda = \frac{6.626}{4} \times 10^{-34 + 3} = 1.6565 \times 10^{-31} \, \text{m} \]

### Step 7: Final result
Thus, the de Broglie wavelength of the rifle bullet is:
\[ \lambda \approx 1.6565 \times 10^{-31} \, \text{m} \]