Atoms and Nuclei

A radioactive X with a half life 1.4 \(\times\) 109 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

An electron in hydrogen atom makes a transition n1 \(\to\) n2 where n1 and n2 are principal quantum numbers of the two states . Assuming Bohr's model to be valid, the time period of the electron in the initial state is eight times that in...

\(\alpha\)-particles, \(\beta\)-particles and \(\gamma\)-rays are all having same energy. Their penetrating power in a given medium in increasing order will be

How does the Binding Energy per nucleon vary with the increase in the number of nucleons ?

A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u = 931 MeV)

Ratio of longest wave lengths corresponding to Lyman and Balmer series in hydrogen spectrum is

The half life of a radioactive isotope 'X' is 20 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be

A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A1 and 160 g of A2. The amount of the two in the mixture will become equal after

If the nuclear radius of 27Al is 3.6 fermi, the approximate nuclear radius of 64Cu in fermi 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

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

The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

The half life of a radioactive nucleus is 50 days. The time invertal (t2 \(-\) t1) between the time t2 when \({2 \over 3}\) of it has decayed and the time t1 when \({1 \over 3}\) of it had decayed is

A nucleus \({}_n^mX\) emits one \(\alpha\) particle and two \(\beta\) particles. The resulting nucleus is

The half life of a radioactive isotope X is 50 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

Fusion reaction takes place at high temperature because

The power obtained in a reactor using U235 disintegration is 1000 kW. The mass decay of U235 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 hydrogen like ion is

A radioactive nucleus of mass M emits a photon of frequency \(v\) and the nucleus recoils. The recoil energy will be

An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having work function 2.75 eV. If the stopping potential of the photoelectron is 10 V, then the ...

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0. number of P species are 4 N0 and that of Q are N0. Half -life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially ...

Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model?

The energy of a hydrogen atom in the ground state is \(-\) 13.6 eV. The energy of a He+ ion in the first excited state will be

An alpha nucleus of energy \({1 \over 2}\) mv2 bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

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

The activity of a radioactive sample is measured as N0 counts per minute at t = 0 and N0/e counts per minute at t = 5 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 eV. The energy of a He+ ion in the first excited state will be

The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

The decay constant of a radio isotope is \(\lambda\). If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1 \(-\) t2)

The ionization energy of the electron in the hydrogen atom in its ground state is 13.6 eV. The atoms are excited to higher energy levels to emit radiations of 6 wavelengths, Maximum wavelength of emitted radiation corresponds to the transit...

In a Rutherford scattering experiment when a projectile of charge z1 and mass M1 approaches a target nucleus of charge z2 and mass M2, the distance of closest approach is r0. The energy of the projectile is

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an

In the nuclear decay given below
\({}_Z^AX \to {}_{Z + 1}^AY \to {}_{Z - 1}^{A - 4}B{}^ * \to {}_{Z - 1}^{A - 4}B,\)
the particles emitted in the sequence are

If M(A; Z), Mp and Mn denote the masses of the nucleus \({}_Z^AX,\) proton and neutron respectively in units of u (1 u = 931.5 MeV/c2) and BE represents its bonding energy in MeV, then

Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be

The ground state energy of hydrogen atom is \(-\) 13.6 eV. When its electron is in the first excited state, its excitation energy is

Two radioactive materials X1 and X2 have decay constants \(5\lambda\) and \(\lambda\) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that X2 will be 1/e after a time

A nucleus \({}_Z^AX\) has mass represented by M(A, Z). If Mp and Mn denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then

In a radioactive decay process, the negatively charged emitted \(\beta\)-particles are

Two radioactive substances A and B have decay constants 5\(\lambda\) and \(\lambda\) respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e)2 after a time interval

The total energy of electron in the ground state of hydrogen atom is \(-\) 13.6 eV. The kinetic energy of an electron in the first excited state 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 semicircular paths of radius R using a magnetic field B. If V and B are kept constant,...

If the nucleus \({}_{13}^{27}Al\) has a nuclear radius of about 3.6 fm, them \({}_{32}^{125}Te\) would have its radius approximately as

The binding energy of deuteron is 2.2 MeV and that of \({}_2^4\)He is 28 MeV. If two deuterons are fused to form one \({}_2^4\)He then the energy released is

The radius of germanium (Ge) nuclide is measured to be twice the radius of \({}_4^9\)Be. The number of nucleons in Ge are

In a radioactive material the activity at time t1 is R1 and at a later time t2, it is R2. If the decay constant of the material is \(\lambda\), then

Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emited by hydrogen will be

Fission of nuclei is possible because the binding energy per nucleon in them

The total energy of an electron in the first excited state of hydrogen atom is about \(-\) 3.4 eV. Its kinetic energy in this state is

Energy levels A, B and C of a certain atom corresponding to increasing values of energy i.e. EA < EB < EC. If \(\lambda\)1, \(\lambda\)2 and \(\lambda\)3 are wavelengths of radioations corresponding to transitions C to B, B to A and C ...