The wavelength of a moving body of mass `0.1 mg` is `3.31xx10^(-29) m`. The kinetic energy of the body in J would be :

Answer

To find the kinetic energy of a moving body given its wavelength, we can follow these steps:

### Step 1: Convert the mass to kilograms
The mass of the body is given as 0.1 mg. We need to convert this to kilograms:
\[ \text{Mass} (m) = 0.1 \, \text{mg} = 0.1 \times 10^{-3} \, \text{g} = 0.1 \times 10^{-6} \, \text{kg} = 10^{-7} \, \text{kg} \]

### Step 2: Use the de Broglie wavelength formula
The de Broglie wavelength (\(\lambda\)) is related to the momentum (\(p\)) of the body by the formula:
\[ \lambda = \frac{h}{p} \]
where \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)). Rearranging this gives us:
\[ p = \frac{h}{\lambda} \]

### Step 3: Substitute the values to find momentum
Now we can substitute the values of \(h\) and \(\lambda\):
\[ p = \frac{6.626 \times 10^{-34}}{3.31 \times 10^{-29}} \]
Calculating this gives:
\[ p = 2.00 \times 10^{-5} \, \text{kg m/s} \]

### Step 4: Calculate the kinetic energy
The kinetic energy (\(KE\)) is given by the formula:
\[ KE = \frac{p^2}{2m} \]
Substituting the values of \(p\) and \(m\):
\[ KE = \frac{(2.00 \times 10^{-5})^2}{2 \times (10^{-7})} \]
Calculating \(p^2\):
\[ (2.00 \times 10^{-5})^2 = 4.00 \times 10^{-10} \]
Now substituting this into the kinetic energy formula:
\[ KE = \frac{4.00 \times 10^{-10}}{2 \times 10^{-7}} = \frac{4.00 \times 10^{-10}}{2.00 \times 10^{-7}} = 2.00 \times 10^{-3} \, \text{J} \]

### Final Answer
The kinetic energy of the body is:
\[ \text{KE} = 2.00 \times 10^{-3} \, \text{J} \]

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