Modern Physics Questions

A particle of mass $m$ is moving around the origin with a constant force $F$ pulling it towards the origin. If Bohr model is used to describe its motion, the radius $r$ of the $n^{th}$ orbit and the particle's speed $v$ in the orbit depend on $n$ as:

De-Broglie wavelength of an electron orbiting in the $n=2$ state of hydrogen atom is close to (Given Bohr radius $=0.052\text{nm}$):

A photon and an electron (mass $m$) have the same energy $E$. The ratio $({\lambda }_{\text{photon}}/{\lambda }_{\text{electron}})$ of their de-Broglie wavelengths is ($c$ is the speed of light):

Which of the following options represents the variation of photoelectric current with intensity and frequency of light shown on the x-axis?

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes $n=2\to n=3$ and $n=4\to n=6$ transitions, respectively, is:

Energy and radius of first Bohr orbit of $H{e}^{+}$ and $L{i}^{2+}$ are:[Given $R_H=2.18\times 10^{-18}\text{J},a_0=52.9\text{pm}$ ]

A model for quantized motion of an electron in a uniform magnetic field $B$ states that the flux passing through the orbit of the electron is $n(h/e)$ where $n$ is an integer, $h$ is Planck's constant and $e$ is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ($m$ is the mass of the electron):

A radioactive nucleus of mass $M$ emits a photon of frequency $\nu$ and the nucleus recoils. The recoil energy will be:

Electrons used in an electron microscope are accelerated by a voltage of $25\text{kV}$. If the voltage is increased to $100\text{kV}$, then the de-Broglie wavelength associated with the electrons would:

The power obtained in a reactor using ${\text{U}}^{235}$ disintegration is $1000\text{kW}$. The mass decay of ${\text{U}}^{235}$ per hour is:

The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen-like ion. The atomic number $Z$ of the hydrogen-like ion is:

In photoelectric emission process from a metal of work function $1.8\text{eV}$, the kinetic energy of most energetic electrons is $0.5\text{eV}$. The corresponding stopping potential is:

Light of two different frequencies whose photons have energies $1\text{eV}$ and $2.5\text{eV}$ respectively illuminate a metallic surface whose work function is $0.5\text{eV}$ successively. The ratio of maximum speeds of emitted electrons will be:

In the Davisson and Germer experiment, the velocity of electrons emitted from the electron gun can be increased by:

The half-life of a radioactive isotope $X$ is $50\text{years}$. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1:15$ in a sample of a given rock. The age of the rock was estimated to be:

Photoelectric emission occurs only when the incident light has more than a certain minimum:

Fusion reaction takes place at high temperature because:

A nucleus ${}_n^{m}X$ emits one $\alpha$ particle and two $\beta$ -particles. The resulting nucleus is:

Hydrogen atom in ground state is excited by a monochromatic radiation of $\lambda =975\text{A˚}$. Number of spectral lines in the resulting spectrum emitted will be:

If the nuclear radius of ${}^{27}\text{Al}$ is $3.6\text{Fermi}$, the approximate nuclear radius of ${}^{64}\text{Cu}$ in Fermi is:

An $\alpha$ -particle moves in a circular path of radius $0.83\text{cm}$ in the presence of a magnetic field of $0.25{\text{Wb/m}}^2$. The de Broglie wavelength associated with the particle will be:

A $200\text{W}$ sodium street lamp emits yellow light of wavelength $0.6\mu \text{m}$. Assuming it to be $25\%$ efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is:

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be:

Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates a photosensitive material. The stopping potential is measured to be $3.57\text{V}$. The threshold frequency of the material is:

A mixture consists of two radioactive materials $A_1$ and $A_2$ with half-lives of $20\text{s}$ and $10\text{s}$ respectively. Initially the mixture has $40\text{g}$ of $A_1$ and $160\text{g}$ of $A_2$. The amount of the two in the mixture will become equal after:

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths ${\lambda }_1:{\lambda }_2$ emitted in the two cases is:

An alternating electric field, of frequency $\nu$, is applied across the dees (radius $=R$) of a cyclotron that is being used to accelerate protons (mass $=m$). The operating magnetic field ($B$) used in the cyclotron and the kinetic energy ($K$) of the proton beam are:

Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is:

The half-life of a radioactive isotope 'X' is $20\text{years}$. It decays to stable element 'Y'. The ratio of 'X' to 'Y' in a rock is $1:7$. The age of the rock is:

Mass defect in a fusion reaction of Hydrogen to Helium is $0.02866\text{u}$. The energy liberated per nucleon is approximately: (Given $1\text{u}=931\text{MeV}$)

For photoelectric emission, the cutoff frequency is $\nu$. If radiation of frequency $2\nu$ impinges on the plate, the maximum velocity of emitted electrons is:

The wavelength ${\lambda }_e$ of an electron and ${\lambda }_p$ of a photon of same energy $E$ are related by:

When the energy of the incident radiation is increased by $20\%$, the kinetic energy of the photoelectrons emitted from a metal surface increased from $0.5\text{eV}$ to $0.8\text{eV}$. The work function of the metal is:

If the kinetic energy of the particle is increased to $16$ times its previous value, the percentage change in the de-Broglie wavelength of the particle is:

Transition $n=3$ to $n=1$ results in ultraviolet radiation. Infrared radiation will be obtained in:

The Binding energy per nucleon of ${}_3^7\text{Li}$ and ${}_2^4\text{He}$ nuclei are $5.60\text{MeV}$ and $7.06\text{MeV}$, respectively. In the nuclear reaction ${}_3^7\text{Li}{+}_1^1\text{H}\to 2_2^4\text{He}+Q$, the value of energy $Q$ released is:

A radio isotope 'X' with a half life $1.4\times 10^9\text{years}$ decays to 'Y' which is stable. A sample of the rock from a cave was found to contain 'X' and 'Y' in the ratio $1:7$. The age of the rock is:

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

In the given figure, a diode $D$ is connected to an external resistance $R=100\Omega$ and an e.m.f. of $3.5\text{V}$. If the barrier potential developed across the diode is $0.5\text{V}$, the current in the circuit will be:

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

Light of wavelength $500\text{nm}$ is incident on a metal with work function $2.28\text{eV}$. The de Broglie wavelength of the emitted electron is:

A photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $\frac{\lambda }{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is $3$ times that in the first case, the work function of the surface of the material is:

When a metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is $V$. If the same surface is illuminated with radiation of wavelength $2\lambda$, the stopping potential is $V/4$. The threshold wavelength for the metallic surface is:

Given the value of Rydberg constant is $10^7{\text{m}}^{-1}$, the wave number of the last line of the Balmer series in hydrogen spectrum will be:

An electron of mass $m$ and a photon have same energy $E$. The ratio of de-Broglie wavelengths associated with them is:

When an $\alpha$ -particle of mass $m$ moving with velocity $v$ bombards on a heavy nucleus of charge $Ze$, its distance of closest approach from the nucleus depends on $m$ as:

Electrons of mass $m$ with de-Broglie wavelength $\lambda$ fall on the target in an X-ray tube. The cutoff wavelength (${\lambda }_0$) of the emitted X-ray is:

Photons with energy $5\text{eV}$ are incident on a cathode $C$ in a photoelectric cell. The maximum energy of emitted photoelectrons is $2\text{eV}$. When photons of energy $6\text{eV}$ are incident on $C$, no photoelectrons will reach the anode $A$, if the stopping potential of $A$ relative to $C$ is:

If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength $\lambda$. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be:

The half-life of a radioactive substance is $30\text{minutes}$. The time (in minutes) taken between $40\%$ decay and $85\%$ decay of the same radioactive substance is:

Which is not a possible energy for a photon emitted by $\text{H}$ -atom?

The ionization energy of the electron in the hydrogen atom in its ground state is $13.6\text{eV}$. The atoms are excited to higher energy levels to emit radiations of $6$ wavelengths. Maximum wavelength of emitted radiation corresponds to the transition between:

A source $S_1$ is producing $10^{15}\text{ photons per second}$ of wavelength $5000\text{ A˚}$. Another source $S_2$ is producing $1.02\times 10^{15}\text{ photons per second}$ of wavelength $5100\text{ A˚}$. Then (power of $S_2$)/(power of $S_1$) is equal to:

A beam of cathode rays is subjected to crossed Electric ($E$) and Magnetic field ($B$). The fields are adjusted such that the beam is not deflected. The specific charge ($e/m$) of the cathode rays is given by (where $V$ is the potential difference between cathode and anode):

The potential difference that must be applied to stop the fastest photo electrons emitted by a nickel surface, having work function $5.01\text{ eV}$, when ultraviolet light of $200\text{ nm}$ falls on it, must be:

The activity of a radioactive sample is measured as $N_0\text{ counts per minute}$ at $t=0$ and $N_0/e\text{ counts per minute}$ at $t=5\text{ minutes}$. The time (in minutes) at which the activity reduces to half its value is:

The energy of a hydrogen atom in the ground state is $-13.6\text{ eV}$. The energy of a ${\text{He}}^{+}$ ion in the first excited state will be:

The mass of a ${}_3^7\text{Li}$ nucleus is $0.042\text{ u}$ less than the sum of the masses of all its nucleons. The binding energy per nucleon of ${}_3^7\text{Li}$ nucleus is nearly:

An alpha nucleus of energy $\frac{1}{2}m{v}^2$ bombards a heavy nuclear target of charge $Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to:

A common emitter amplifier has a voltage gain of $50$, an input impedance of $100\Omega$ and an output impedance of $200\Omega$. The power gain of the amplifier is:

Which one of the following bonds produces a solid that reflects light in the visible region and whose electrical conductivity decreases with temperature and has high melting point?

The device that can act as a complete electronic circuit is:

Which of the following statements is False?

To get an output $Y=1$ from the circuit shown below, the input must be ($A,B,C$):

Threshold frequency for a metal is $3.3\times 10^{14}\text{Hz}$. If light of frequency $8.2\times 10^{14}\text{Hz}$ is incident, the cut-off voltage is nearly:

An electron in $\text{H}$ -atom jumps from $n$ to ground state. Work function of material is $2.75\text{eV}$ and stopping potential is $10\text{V}$. The value of $n$ is:

Monochromatic light of wavelength $667\text{nm}$ is produced by a helium neon laser. The power emitted is $9\text{mW}$. The number of photons arriving per sec. on the average at a target irradiated by this beam is:

Two nuclei $P$ ($4N_0,T_{1/2}=1\text{m}$) and $Q$ ($N_0,T_{1/2}=2\text{m}$) decay to $R$. When $P=Q$, the number of $R$ nuclei present is:

In a Rutherford scattering experiment when a projectile of charge $z_1$ and mass $M_1$ approaches a target nucleus of charge $z_2$ and mass $M_2$, the distance of closest approach is $r_0$. The energy of the projectile is:

The Figure shows a plot of photo current versus anode potential for a photo sensitive surface for three different radiations. Which one of the following is a correct statement?

A p-n photodiode is fabricated from a semiconductor with a band gap of $2.5\text{eV}$. It can detect a signal of wavelength:

The number of photo electrons emitted for light of a frequency $\nu$ (higher than the threshold frequency ${\nu }_0$) is proportional to:

A p-n photodiode is made of a material with a band gap of $2.0\text{eV}$. The minimum frequency of the radiation that can be absorbed by the material is nearly:

A particle of mass $1\text{mg}$ has the same wavelength as an electron moving with a velocity of $3\times 10^6{\text{ms}}^{-1}$. The velocity of the particle is ($mass$ $of$ $electron=9.1\times 10^{-31}\text{kg}$):

The work function of a surface of a photosensitive material is $6.2\text{eV}$. The wavelength of the incident radiation for which the stopping potential is $5\text{V}$ lies in the:

Monochromatic light of frequency $6.0\times 10^{14}\text{Hz}$ is produced by a laser. The power emitted is $2\times 10^{-3}\text{W}$. The number of photons emitted, on the average, by the source per second is:

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential $V$ and then made to describe semi-circular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant, the ratio $\frac{q}{m}$ will be proportional to:

The total energy of electron in the ground state of hydrogen atom is $-13.6\text{eV}$. The kinetic energy of an electron in the first excited state is:

A $5\text{W}$ source emits monochromatic light of wavelength $5000\text{A˚}$. When placed $0.5\text{m}$ away, it liberates photoelectrons from a photosensitive metallic surface. When the source is moved to a distance of $1.0\text{m}$, the number of photoelectrons liberated, will be reduced by a factor of:

Two radiations of photon energies $1\text{eV}$ and $2.5\text{eV}$ illuminate a surface of work function $0.5\text{eV}$ successively. The ratio of the maximum speeds of the emitted electrons is:

Half life is $50$ days. Time interval $(t_2-t_1)$ between when $2/3$ has decayed and $1/3$ has decayed is: