An electron (mass m) with an initial velocity `vecv=v_(0)hati` is in an electric field `vecE=E_(0)hatj`. If `lambda_(0)=h//mv_(0)`. It's de-broglie wavelength at time t is given by

Options

A. `lamda_(0)`
B. `lamda_(0)sqrt(1+(e^(2)E_(0)^(2)t^(2))/(m^(2)v_(0)^(2)))`
C. `(lamda_(0))/(sqrt(1+(e^(2)E_(0)^(2)t^(2))/(m^(2)v_(0)^(2))))`
D. `(lamda_(0))/(1+(e^(2)E_(0)^(2)t^(2))/(m^(2)v_(0)^(2)))`

Explanation

To find the de Broglie wavelength of an electron in an electric field at time \( t \), we will follow these steps:

### Step 1: Identify the forces acting on the electron
The electron has an initial velocity \( \vec{v} = v_0 \hat{i} \) and is in an electric field \( \vec{E} = E_0 \hat{j} \). The force acting on the electron due to the electric field is given by:
\[ \vec{F} = q \vec{E} \]
Since the charge of the electron is \( -e \), the force becomes:
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