JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
An electron of mass \(m\) is moving in an electric field \(\vec{E} = -2E_0\hat{i}\) (\(E_0 =\) constant \(> 0\)), with an initial velocity \(\vec{V} = v_0\hat{i}\) (\(v_0 =\) constant \(> 0\)). If \(\lambda_0 = \dfrac{h}{4mv_0}\), its de Broglie wavelength at time \(t\) is __________.
(\(e =\) charge of electron)
- A \(\dfrac{4\lambda_0}{\left[1 - \dfrac{E_0 e}{2m}\dfrac{t}{v_0}\right]}\)
- B \(\dfrac{4\lambda_0}{\left[1 + \dfrac{E_0 e}{2m}\dfrac{t}{v_0}\right]}\)
- C \(\dfrac{4\lambda_0}{\left[1 + \dfrac{2E_0 e}{m}\dfrac{t}{v_0}\right]}\)
- D \(\dfrac{4\lambda_0}{\left[1 - \dfrac{2E_0 e}{m}\dfrac{t}{v_0}\right]}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{4\lambda_0}{\left[1 + \dfrac{2E_0 e}{m}\dfrac{t}{v_0}\right]}\)
Step-by-step Solution
Detailed explanation
The force experienced by the electron in the electric field is given by \(\vec{F} = q\vec{E}\). Since the charge of an electron is \(-e\) and the electric field is \(\vec{E} = -2E_0\hat{i}\), the force is: \(\vec{F} = (-e)(-2E_0\hat{i}) = 2eE_0\hat{i}\) The acceleration of the…
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