The de Broglie wavelength of a ball of mass 10g moving with a velocity of `10 ms^(-1)` is `(h = 6.626 xx 10^(-34) Js)`

Options

A. `6.626 xx 10^(-33) m`
B. `6.626 xx 10^(-29) m`
C. `6.626 xx 10^(-31) m`
D. `6.626 xx 10^(-36) m`

Answer

To find the de Broglie wavelength of a ball with a mass of 10 grams moving at a velocity of 10 m/s, we can use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the de Broglie wavelength,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(p\) is the momentum of the object.

### Step 1: Convert mass from grams to kilograms
The mass of the ball is given as 10 grams. To use SI units, we need to convert this to kilograms:

\[ \text{Mass} = 10 \, \text{g} = \frac{10}{1000} \, \text{kg} = 0.01 \, \text{kg} \]

### Step 2: Calculate the momentum
Momentum \(p\) is calculated using the formula:

\[ p = m \cdot v \]

where:
- \(m\) is the mass in kg,
- \(v\) is the velocity in m/s.

Substituting the values:

\[ p = 0.01 \, \text{kg} \cdot 10 \, \text{m/s} = 0.1 \, \text{kg m/s} \]

### Step 3: Calculate the de Broglie wavelength
Now we can substitute the values of \(h\) and \(p\) into the de Broglie wavelength formula:

\[ \lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34} \, \text{Js}}{0.1 \, \text{kg m/s}} \]

Calculating this gives:

\[ \lambda = 6.626 \times 10^{-34} \, \text{Js} \div 0.1 \, \text{kg m/s} = 6.626 \times 10^{-33} \, \text{m} \]

### Final Answer
The de Broglie wavelength of the ball is:

\[ \lambda = 6.626 \times 10^{-33} \, \text{m} \]

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