Atoms and Nuclei

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited sta...

Half-lives of two radioactive elements \(A\) and \(B\) are \(20\) minutes and \(40\) minutes, respectively. Initially, the samples have equal number of nuclei. After \(80\) minutes, the ratio of decayed number of \(A\) and \(B\) nuclei will...

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C14 is 5730 years, then age of the wo...

Match List - I (Experiment performed) with List - II (Phenomena discovered/associated) and select the correct option from the options given below the lists :

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Hydrogen \(\left( {{}_1{H^1}} \right)\), Deuterium \(\left( {{}_1{H^2}} \right)\), singly ionised Helium \({\left( {{}_2H{e^4}} \right)^ + }\) and doubly ionised lithium \({\left( {{}_3L{i^6}} \right)^{ + + }}\) all have one electron aroun...

The radiation corresponding to \(3 \to 2\) transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field \(3 \times {10^{ - 4}}\,T.\) If the radius of the larger circular ...

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

A diatomic molecule is made of two masses \({m_1}\) and \({m_2}\) which are separated by a distance \(r.\) If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by: (\(n\) i...

Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron \(= 1.6725 \times {10^{ - 27}}kg,\) mass of proton \(= 1.6725 \times {10^{ - 27}}\,kg,\) mass of electron $$ = 9 \t...

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

Energy required for the electron excitation in \(L{i^{ + + }}\) from the first to the third Bohr orbit is :

A radioactive nucleus (initial mass number \(A\) and atomic number \(Z\) emits \(3\,\alpha\)- particles and \(2\) positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

A nucleus of mass \(M+\)\(\Delta m\) is at rest and decays into two daughter nuclei of equal mass \({M \over 2}\) each. Speed of light is \(c.\)
The speed of daughter nuclei is

A nucleus of mass \(M+\)\(\Delta m\) is at rest and decays into two daughter nuclei of equal mass \({M \over 2}\) each. Speed of light is \(c.\)
The binding energy per nucleon for the parent nucleus is \({E_1}\) and that for the daughter n...

The above is a plot of binding energy per nucleon \({E_b},\) against the nuclear mass \(M;A,B,C,D,E,F\) correspond to different nuclei. Consider four reactions :
$$\eqalign{
& \left( i \right)\,\,\,\,\,\,\,\,\,\,A + B \to C + \varepsil...

The transition from the state \(n=4\) to \(n=3\) in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the transition from :

This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two statements:
Statement- 1:
Energy is released when heavy nuclei undergo fission or light nucl...

Suppose an electron is attracted towards the origin by a force \({k \over r}\) where \('k'\) is a constant and \('r'\) is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the \({n^{th}}\) or...

In gamma ray emission from a nucleus

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

If \({M_O}\) is the mass of an oxygen isotope \({}_8{O^{17}}\) , \({M_p}\) and \({M_N}\) are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is

The half-life period of a ratio-active element \(X\) is same as the mean life time of another ratio-active element \(Y.\) Initially they have the same number of atoms. Then

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

The \('rad'\) is the correct unit used to report the measurement of

If the binding energy per nucleon in \({}_3^7Li\) and \({}_2^4He\) nuclei are \(5.60\) \(MeV\) and \(7.06\) \(MeV\) respectively, then in the reaction
\($p + {}_3^7Li \to 2\,{}_2^4He\)$
energy of proton must be

When \({}_3L{i^7}\) nuclei are bombarded by protons, and the resultant nuclei are \({}_4B{e^8}\), the emitted particles will be

The energy spectrum of \(\beta\)-particles [ number \(N(E)\) as a function of \(\beta\)-energy \(E\) ] emitted from a radioactive source is

Starting with a sample of pure \({}^{66}Cu,{7 \over 8}\) of it decays into \(Zn\) in \(15\) minutes. The corresponding half life is

The intensity of gamma radiation from a given source is \(L\). On passing through \(36\) \(mm\) of lead, it is reduced to \({{\rm I} \over 8}.\) The thickness of lead which will reduce the intensity to \({{\rm I} \over 2}\) will be

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?

A nuclear transformation is denoted by \(X\left( {n,\alpha } \right)\matrix{ 7 \cr 3 \cr } Li.\) Which of the following is the nucleus of element \(X\) ?

If radius of the \(\matrix{ {27} \cr {13} \cr }\) \(Al\) nucleus is estimated to be \(3.6\) fermi then the radius of \(\matrix{ {125} \cr {52} \cr } \,Te\) nucleus is estimated to be nearly

A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of \(2:1.\) The ratio of their nuclear sizes will be

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

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

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

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

If the binding energy of the electron in a hydrogen atom is \(13.6eV,\) the energy required to remove the electron from the first excited state of \(L{i^{ + + }}\) is

In the nuclear fusion reaction
\(${}_1^2H + {}_1^3H \to {}_2^4He + n\)$
given that the repulsive potential energy between the two nuclei is \(\sim 7.7 \times {10^{ - 14}}J\), the temperature at which the gases must be heated to initiate t...

Which of the following radiations has the least wavelength ?

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

Which of the following atoms has the lowest ionization potential ?

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

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

If \(13.6\) \(eV\) energy is required to ionize the hydrogen atom, then the energy required to remove an electron from \(n=2\) is

At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit
$$\eqalign{
& \left( i \right)\,\,\,\,\,\,\,electrons\,\,\,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,protons \cr
...

If \({N_0}\) is the original mass of the substance of half-life period \({t_{1/2}} = 5\) years, then the amount of substance left after \(15\) years is