An electron of mass m with an initial velocity v = v₀i (v0 > 0) enters an electric field E = -E₀i (E0 = constant > 0) at t = 0. If λ 0 is its de-Broglie wavelength initially, then its de- Broglie wavelength at time t is (a) (λ₀)/((1+(eE₀)/(mv₀)t)) (b) λ₀(1 + (eE₀)/(mv₀)t) (c) λ 0t (d) λ 0

Answer: (a). Force on electron F = -e E = +eE₀ i, along v: it speeds up. v = v₀ + eE₀/mt λ = h/mv = (h)/(mv₀(1+(eE₀)/(mv₀)t)) = (λ₀)/(1+(eE₀)/(mv₀)t) So the answer is (a).

An electron of mass m with an initial velocity v = v₀i (v0 > 0)… | NEET 2018

Q128NEET 2018Medium

Matter Waves: de Broglie Wavelength

An electron of mass m with an initial velocity $\vec{v} = v_0\hat{i}$ (v0 > 0) enters an electric field $\vec{E} = -\vec{E}_0\hat{i}$ (E0 = constant > 0) at t = 0. If $\lambda$ 0 is its de-Broglie wavelength initially, then its de- Broglie wavelength at time t is

Show answer and solution

Answer: (a)

Force on electron $\vec F = -e\vec E = +eE_0\hat i$ , along $\vec v$ : it speeds up.
$v = v_0 + \dfrac{eE_0}{m}t$
$\lambda = \dfrac{h}{mv} = \dfrac{h}{mv_0\left(1+\frac{eE_0}{mv_0}t\right)} = \dfrac{\lambda_0}{1+\frac{eE_0}{mv_0}t}$
So the answer is (a).

Report a mistake

Matter Waves: de Broglie Wavelength question from NEET 2018

More questions on Matter Waves: de Broglie Wavelength