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JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
An electron of mass m with an initial velocity \(\overrightarrow{ V }= V_0 \hat i \,(V_0 > 0)\) enters an electric field \(\vec E = -\vec E_0 \hat i \,(E_0 =\) constant \(> 0)\) at \(t = 0.\) If \(\lambda_0\) is its de-Broglie wavelength initially,then its de-Broglie wavelenght at time \(t\) is
- A \(\frac{{{\lambda _0}}}{{\left( {1 + \frac{{e{E_0}}}{{m{V_0}}}t} \right)}}\)
- B \({\lambda _0}\;\left( {1 + \frac{{e{E_0}}}{{m{V_0}}}t} \right)\)
- C \({\lambda _0}\)
- D \({\lambda _0}t\)
Answer & Solution
Correct Answer
(A) \(\frac{{{\lambda _0}}}{{\left( {1 + \frac{{e{E_0}}}{{m{V_0}}}t} \right)}}\)
Step-by-step Solution
Detailed explanation
Here, \(\vec{E}=-E_{0} \hat{i} ;\) initial velocity \(\vec{v}=v_{0} \hat{i}\) Force action on electron due to electric field \(\bar{F}=(-e)\left(-E_{0} \hat{i}\right)=e E_{0} \hat{i}\) Acceleration produced in the electron, \(\vec{a}=\frac{\vec{F}}{m}=\frac{e E_{0}}{m} \hat{i}\)…
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