Modern Physics Questions

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:

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 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:

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:

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

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:

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

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:

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:

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

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:

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:

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:

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:

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 $\alpha$ -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:

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

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

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

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

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:

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:

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

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:

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:

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

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:

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:

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

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: