Relativistic corrections become necessary when the expression for the kinetic energy `1/2mv^(2)`, becomes comparable with `mc^(2)`, where m is the mass of the particle. At what de-broglie wavelength will relativistic corrections become important for an electron?

Options

A. `lamda=10nm`
B. `lamda=10^(-1)nm`
C. `lamda=10^(-4)nm`
D. `lamda=10^(-6)nm`

Explanation

To determine at what de Broglie wavelength relativistic corrections become important for an electron, we start by comparing the kinetic energy expression \( \frac{1}{2}mv^2 \) with the rest energy \( mc^2 \). Relativistic effects become significant when the kinetic energy is comparable to the rest energy.

### Step-by-Step Solution:

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