JEE Main 2013 — Modern Physics

Electrons are accelerated through a potential difference $\mathrm{V}$ and protons are accelerated through a potential difference $4 \mathrm{~V}$. The de-Broglie wavelengths are $\lambda_e$ and $\lambda_p$ for electrons and protons respectively. The ratio of $\frac{\lambda_e}{\lambda_p}$ is given by: (given $m_e$ is mass of electron and $m_p$ is mass of proton).

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $\text{I}$ of the photocell varies as follows :

When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as : ${ }_{92} \mathrm{U}^{235}+{ }_0 n^1 \rightarrow{ }_{56} \mathrm{Ba}^{141}+{ }_{36} \mathrm{Kr}^{92}+3 x+\mathrm{Q}($ energy) where three particles named $x$ are produced and energy $\mathrm{Q}$ is released. What is the name of the particle $x$ ?

In the Bohr model an electron moves in a circular orbit around the proton. Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in $n^{\text {th }}$ excited state, is :

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the $n^{\text {th }}$ orbital will therefore be proportional to :

In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as $F=\frac{e^2}{4 \pi \varepsilon_0}\left(\frac{1}{r^2}+\frac{\beta}{r^3}\right)$, where $\beta$ is a constant. For this atom, the radius of the $n^{\text {th }}$ orbit in terms of the Bohr radius $\left(a_0=\frac{\varepsilon_0 h^2}{m \pi e^2}\right)$ is :

The $\text{I} - \text{V}$ characteristics of an $\text{LED}$ is:

In a hydrogen like atom electron makes transition from an energy level with quantum number $\text{n}$ to another with quantum number $( \text{n} - 1 )$. If $\text{n >> 1}$, the frequency of radiation emitted is proportional to :

A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance of 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.

Consider two npn transistors as shown in figure. If 0 Volts corresponds to false and 5 Volts correspond to true then the output at C corresponds to : 

A copper ball of radius $1 \mathrm{~cm}$ and work function $4.47 \mathrm{~eV}$ is irradiated with ultraviolet radiation of wavelength $2500 ~Å$. The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is :

A $12.5 \mathrm{eV}$ electron beam is used to bombard gaseous hydrogen at room temperature. It will emit:

Figure shows a circuit in which three identical diodes are used. Each diode has forward resistance of $20 \Omega$ and infinite backward resistance. Resistors $\mathrm{R}_1=\mathrm{R}_2=\mathrm{R}_3=50 \Omega$. Battery voltage is $6 \mathrm{~V}$. The current through $\mathrm{R}_3$ is : 

A system of four gates is set up as shown. The 'truth table' corresponding to this system is : 

In an experiment on photoelectric effect, a student plots stopping potential $\mathrm{V}_0$ against reciprocal of the wavelength $\lambda$ of the incident light for two different metals $\mathrm{A}$ and $\mathrm{B}$. These are shown in the figure.  Looking at the graphs, you can most appropriately say that:

Which of the following circuits correctly represents the following truth table ?