A ball has a mass of 0.1 kg its velocity is 40 m/s, find out de Broglie wave length -

Options

A. `1.66 x 10 ^(-34) m`
B. ` 2x 10 ^(-34)m`
C. `3 x 10 ^(-34)m`
D. `4 xx 10 ^(-34) m`

Answer

To find the de Broglie wavelength of a ball with a mass of 0.1 kg and a velocity of 40 m/s, we can follow these steps:

### Step 1: Write down the formula for de Broglie wavelength
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \))
- \( m \) is the mass of the object (in kg)
- \( v \) is the velocity of the object (in m/s)

### Step 2: Identify the values from the question
From the question, we have:
- Mass \( m = 0.1 \, \text{kg} \)
- Velocity \( v = 40 \, \text{m/s} \)

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the de Broglie wavelength formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{0.1 \times 40} \]

### Step 4: Calculate the denominator
First, calculate the product of mass and velocity:
\[ mv = 0.1 \times 40 = 4 \, \text{kg m/s} \]

### Step 5: Calculate the de Broglie wavelength
Now substitute this value back into the equation:
\[ \lambda = \frac{6.626 \times 10^{-34}}{4} \]
\[ \lambda = 1.6565 \times 10^{-34} \, \text{m} \]

### Step 6: Round off the answer
Rounding off the value, we get:
\[ \lambda \approx 1.66 \times 10^{-34} \, \text{m} \]

### Final Answer
Thus, the de Broglie wavelength of the ball is:
\[ \lambda = 1.66 \times 10^{-34} \, \text{m} \]

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