An electron (mass m ) with initial velocity v=v_0 i+v_0 j is in an electric filed E=-E_0 k. If λ _0 is initial de-Broglie wavelength of electron, its…

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)

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are $10^{15}\text{ atoms/cm}^3$ and $10^{18}\text{ atoms/cm}^3$, respectively. Which one of the following statements is true ?

The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at $V_{z}=5 \mathrm{~V}$ and the desired current in load is 5 mA. The unregulated voltage source can supply upto 25 V. Considering the Zener diode can withstand four times of the load current, the value of resistor $R_{S}$ (shown in circuit) should be $\_\_\_\_$ $\Omega$. 

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The electromagnetic wave exerts pressure on the surface on which they are allowed to fall. Reason (R): There is no mass associated with the electromagnetic waves. In the light of the above statements, choose the correct answer from the options given below :

In hydrogen atom spectrum, $(R \rightarrow$ Rydberg's constant $)$ A. the maximum wavelength of the radiation of Lyman series is $\frac{4}{3 R}$ B. the Balmer series lies in the visible region of the spectrum C. the minimum wavelength of the radiation of Paschen series is $\frac{9}{R}$ D. the minimum wavelength of Lyman series is $\frac{5}{4 R}$ Choose the correct answer from the options given below :