Question

An electron (mass m) with an initial velocity
$\vec{v}=v_0\hat{i}(v_0>0)$
is moving in an electric field
$\vec{E}=E_0\hat{i}(E_0>0)$
where E0 is constant. If at t = 0 de Broglie wavelength is
$λ_0=\frac{ℎ}{mv_0}$
, then its de Broglie wavelength after time t is given by

• A. $λ_0$
• B. $λ_0\left(1+\frac{eE_0t}{mv_0}\right)$
• C. $λ_0t$
• D. $\frac{λ_0}{\left(1+\frac{eE_0t}{mv_0}\right)}$

Answer 1

Answer: (D)

$\frac{λ_0}{\left(1+\frac{eE_0t}{mv_0}\right)}$

Answer 2

The correct answer is (D) : $\frac{λ_0}{\left(1+\frac{eE_0t}{mv_0}\right)}$

$∴a_x=\frac{eE_0}{m}\hat{i}$
$∴v(t)=V_0+\frac{eE_0}{m}t$
$∴\frac{λ_0}{λ_2}=\frac{mv}{mV_0}$
$=(1+\frac{eE_0t}{mV_0})$
$⇒λ_2=\frac{λ_0}{\left(1+\frac{eE_0t}{mV_0}\right)}$