A particle moving with kinetic energy `E_(1)` has de Broglie wavelength `lambda_(1)`. Another particle of same mass having kinetic energy `E_(2)` has de Broglie wavelength `lambda_(2). lambda_(2)= 3 lambda_(2)`. Then `E_(2) - E_(1)` is equal to

Options

A. `7E_(1)`
B. `3E_(1)`
C. `8E_(1)`
D. `9E_(1)`

Explanation

To solve the problem, we need to analyze the relationship between the kinetic energy of the particles and their de Broglie wavelengths.

### Step-by-Step Solution:

1. **Understanding de Broglie Wavelength**:
The de Broglie wavelength (\( \lambda \)) of a particle is given by the formula:
\[
\lambda = \frac{h}{\sqrt{2mK}}
...