Modern Physics Questions

An $\alpha$ -particle of energy $5\text{MeV}$ is scattered through $180^{\circ }$ by a fixed uranium nucleus ($Z=92$). The distance of the closest approach is of the order of:

The binding energy per nucleon of deuteron (${}_1^2\text{H}$) and helium nucleus (${}_2^4\text{He}$) is $1.1\text{MeV}$ and $7\text{MeV}$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is:

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2:1$. The ratio of their nuclear sizes will be:

The work function of a substance is $4.0\text{eV}$. Then the longest wavelength of light that can cause photoelectron emission from this substance is approximately:

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal vs the frequency of the incident radiation gives a straight line whose slope:

The time taken by a photoelectron to come out after the photon strikes is approximately:

The threshold frequency for a metallic surface corresponds to an energy of $6.2\text{eV}$, and the stopping potential for a radiation incident on this surface is $5\text{V}$. The incident radiation lies in the:

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 $I$ of the photocell varies as follows:

A photon of frequency $\nu$ has a momentum associated with it. If $c$ is the velocity of light, the momentum is:

If a strong diffraction peak is observed when electrons are incident at an angle ‘$i$ ’ from the normal to the crystal planes with distance ‘$d$ ’ between them, de Broglie wavelength ${\lambda }_{dB}$ of electrons can be calculated by the relationship ($n$ is an integer):

Electrons accelerated by potential $V$ are diffracted from a crystal. If $d=1\text{A˚}$ and $i=30^{\circ }$, $V$ should be about ($h=6.6\times 10^{-34}\text{J s},m_e=9.1\times 10^{-31}\text{kg},e=1.6\times 10^{-19}\text{C}$):

Statement 1: Davisson-Germer experiment established the wave nature of electrons.Statement 2: If electrons have wave nature, they can interfere and show diffraction.

In an experiment, electrons pass through a narrow slit of width ‘$d$ ’. They are detected on a screen at a distance ‘$D$ ’. Which graph correctly represents the number of electrons $N$ detected as a function of the detector position $y$ ($y=0$ corresponds to the middle of the slit)?

Statement - 1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.Statement - 2: For heavy nuclei, binding energy per nucleon increases with increasing $Z$ while for light nuclei it decreases with increasing $Z$.

Suppose an electron is attracted towards the origin by a force $k/r$ where $k$ is a constant. By applying Bohr model, the radius $r_n$ and kinetic energy $T_n$ of the $n^{\text{th}}$ orbital are:

The surface of a metal is illuminated with the light of $400\text{nm}$. The kinetic energy of the ejected photoelectrons was found to be $1.68\text{eV}$. The work function of the metal is ($hc=1240\text{eV nm}$):

Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{max}$. When the ultraviolet light is replaced by X-rays, both $V_0$ and $K_{max}$ increase.Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

If a source of power $4\text{kW}$ produces $10^{20}$ photons/second, the radiation belongs to a part of the spectrum called:

The half life of a radioactive substance is $20\text{minutes}$. The approximate time interval $(t_2-t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and time $t_1$ when $\frac{1}{3}$ of it had decayed is:

Statement-1 : A metallic surface is irradiated by a monochromatic light of frequency $\nu >{\nu }_0$ (the threshold frequency). The maximum kinetic energy and the stopping potential are $K_{max}$ and $V_0$ respectively. If the frequency incident on the surface is doubled, both the $K_{max}$ and $V_0$ are also doubled.Statement-2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be:

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than $2480\text{ nm}$ is incident on it. The band gap in ($\text{eV}$) for the semiconductor is:

A radioactive sample at any instant has its disintegration rate $5000\text{disintegrations per minute}$. After $5\text{minutes}$, the rate is $1250\text{disintegrations per minute}$. Then, the decay constant (per minute) is:

Which of the following radiations has the least wavelength?

The wavelengths involved in the spectrum of deuterium (${}_1^2\text{D}$) are slightly different from that of hydrogen spectrum, because:

If the binding energy of the electron in a hydrogen atom is $13.6\text{eV}$, the energy required to remove the electron from the first excited state of ${\text{Li}}^{++}$ is:

A nucleus with $Z=92$ emits the following in a sequence: $\alpha ,\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,\alpha ,\alpha ,\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,{\beta }^{+},{\beta }^{+},\alpha$. The $Z$ of the resulting nucleus is:

Two identical photo cathodes receive light of frequencies $f_1$ and $f_2$. If the velocities of the photoelectrons (of mass $m$) coming out are respectively $v_1$ and $v_2$, then:

In the nuclear fusion reaction ${}_1^2\text{H}{+}_1^3\text{H}{\to }_2^4\text{He}+\text{n}$, given that the repulsive potential energy between the two nuclei is $7.7\times 10^{-14}\text{J}$, the temperature at which the gases must be heated to initiate the reaction is nearly: (Boltzmann’s constant $k=1.38\times 10^{-23}\text{J/K}$)

When ${}^{238}\text{U}$ nucleus originally at rest, decays by emitting an alpha particle having a speed $u$, the recoil speed of the residual nucleus is:

Which of the following atoms has the lowest ionization potential?

Which of the following cannot be emitted by radioactive substance during their decay?

A nuclear transformation is denoted by $X(n,\alpha ){}_3^7\text{Li}$. Which of the following is the nucleus of element $X$?

If the kinetic energy of a free electron doubles. Its de Broglie wavelength changes by the factor:

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

If radius of ${}_{13}^{27}\text{Al}$ nucleus is estimated to be $3.6\text{ Fermi}$ then the radius ${}_{52}^{125}\text{Te}$ nucleus be nearly:

Starting with a sample of pure ${}^{66}\text{Cu}$, $7/8$ of it decays into $\text{Zn}$ in $15\text{ minutes}$. The corresponding half-life is:

A photocell is illuminated by a small bright source placed $1\text{ m}$ away. When the same source of light is placed $1/2\text{ m}$ away, the number of electrons emitted by photo cathode would: