An electron (mass m) with initial velocity v =v_ n i +v_ n j is in an elastic field E…
Physics · JEE Main · NTA Exams — Dual Nature of Matter and Radiation
An electron (mass m) with initial velocity \(\vec{v}=v_{n} \hat{i}+v_{n} \hat{j}\) is in an elastic field \(\vec{E}=-E_{\mathbf{n}} \overrightarrow{\mathbf{k}}\). If λ0 is initial de-Broglie wavelength of electron, its de-Broglie wavelength at time t is given by:
- \(\frac{\lambda_{a} \sqrt{2}}{1+\frac{e^{2} E^{2} t^{2}}{m^{2} v_{n}^{2}}}\)
- \(\frac{\lambda_{g}}{\sqrt{z+\frac{e^{2} E^{2} t^{2}}{m^{2} v_{v}^{2}}}}\)
- \(\frac{\lambda_{B}}{\sqrt{1+\frac{e^{2} E^{2} t^{2}}{2 m^{2} v_{B}^{2}}}}\)
- \(\frac{\lambda_{n}}{\sqrt{1+\frac{e^{2} E_{n}^{2} t^{2}}{m^{2} v_{n}^{2}}}}\)
Answer
(D) _ n 1+ e^ 2 E_ n ^ 2 t^ 2 m^ 2 v_ n ^ 2
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