The de Broglie wavelength associated with a ball of mass `1kg` having kinetic enegry `0.5J` is

Options

A. `6.626xx10^(-34)m`
B. `13.20xx10^(-34)m`
C. `10.38xx10^(-21)m`
D. `6.626xx10^(-34)Å`

Explanation

To find the de Broglie wavelength associated with a ball of mass 1 kg and kinetic energy 0.5 J, we can follow these steps:

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

### Step 2: Relate kinetic energy to velocity
The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
From this, we can express the velocity \( v \) in terms of kinetic energy and mass:
\[ v^2 = \frac{2 \times KE}{m} \]
Thus,
\[ v = \sqrt{\frac{2 \times KE}{m}} \]

### Step 3: Substitute the values
Given:
- Mass \( m = 1 \, \text{kg} \)
- Kinetic Energy \( KE = 0.5 \, \text{J} \)

Now substituting the values into the equation for velocity:
\[ v = \sqrt{\frac{2 \times 0.5 \, \text{J}}{1 \, \text{kg}}} \]
\[ v = \sqrt{\frac{1}{1}} = \sqrt{1} = 1 \, \text{m/s} \]

### Step 4: Calculate the de Broglie wavelength
Now substitute \( v \) back into the de Broglie wavelength formula:
\[ \lambda = \frac{h}{mv} \]
Substituting the known values:
\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{1 \, \text{kg} \times 1 \, \text{m/s}} \]
\[ \lambda = 6.626 \times 10^{-34} \, \text{m} \]

### Final Answer
The de Broglie wavelength associated with the ball is:
\[ \lambda = 6.626 \times 10^{-34} \, \text{m} \]