The de Broglie wavelength associated with a ball of mass 150 g travelling at 30 m `s^(-1)` is

Options

A. `1.47xx1^(-34)m`
B. `1.47xx1^(-16)m`
C. `1.47xx1^(-19)m`
D. `1.47xx1^(-31)m`

Explanation

To find the de Broglie wavelength associated with a ball of mass 150 g traveling at 30 m/s, we can follow these steps:

### Step 1: Convert mass from grams to kilograms
The mass of the ball is given as 150 g. To convert this to kilograms:
\[ m = 150 \, \text{g} = 150 \times 10^{-3} \, \text{kg} = 0.150 \, \text{kg} \]

### Step 2: Write down the formula for de Broglie wavelength
The de Broglie wavelength (\(\lambda\)) can be calculated using the formula:
\[ \lambda = \frac{h}{p} \]
where \(h\) is Planck's constant and \(p\) is the momentum of the object.

### Step 3: Calculate momentum
The momentum (\(p\)) of the ball can be calculated using the formula:
\[ p = mv \]
Substituting the values:
\[ p = 0.150 \, \text{kg} \times 30 \, \text{m/s} = 4.5 \, \text{kg m/s} \]

### Step 4: Substitute values into the de Broglie wavelength formula
Now, we substitute the values of \(h\) and \(p\) into the de Broglie wavelength formula. The value of Planck's constant \(h\) is approximately:
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
Thus,
\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{4.5 \, \text{kg m/s}} \]

### Step 5: Calculate the de Broglie wavelength
Now, we perform the division:
\[ \lambda = \frac{6.626 \times 10^{-34}}{4.5} \approx 1.47 \times 10^{-34} \, \text{m} \]

### Final Answer
The de Broglie wavelength associated with the ball is:
\[ \lambda \approx 1.47 \times 10^{-34} \, \text{m} \]

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