If the kinetic energy of a moving particle is E , then the de-Broglie wavelength is

Options

A. `lamda=hsqrt(2mE)`
B. `lamda=sqrt((2mE)/h)`
C. `lamda=h/(sqrt(2mE))`
D. `lamda=(hE)/(sqrt(2mE))`

Answer

To find the de-Broglie wavelength of a moving particle with kinetic energy \( E \), we can follow these steps:

### Step 1: Write the formula for kinetic energy
The kinetic energy \( E \) of a particle is given by the formula:
\[ E = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the particle and \( v \) is its velocity.

### Step 2: Rearrange the kinetic energy formula to find \( mv \)
From the kinetic energy formula, we can express \( mv \) in terms of \( E \):
\[ mv = \sqrt{2mE} \]
This is derived from rearranging the kinetic energy equation. First, multiply both sides by 2:
\[ 2E = mv^2 \]
Then, take the square root:
\[ mv = \sqrt{2mE} \]

### Step 3: Write the formula for de-Broglie wavelength
The de-Broglie wavelength \( \lambda \) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant.

### Step 4: Substitute \( mv \) into the de-Broglie wavelength formula
Now we substitute the expression we found for \( mv \) into the de-Broglie wavelength formula:
\[ \lambda = \frac{h}{\sqrt{2mE}} \]

### Conclusion
Thus, the de-Broglie wavelength of a moving particle with kinetic energy \( E \) is:
\[ \lambda = \frac{h}{\sqrt{2mE}} \]

### Final Answer
The answer is \( \lambda = \frac{h}{\sqrt{2mE}} \).

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