Atoms and Nuclei

The energy released if hydrogen atoms are combined to form $^4_2\mathrm{He}$ is ______ MeV. (Take binding energies per nucleon of $^2_1\mathrm{H}$ and $^4_2\mathrm{He}$ as 1.1 MeV and 7.2 MeV, respectively)

The binding energy per nucleon of ${}^{209}_{83}Bi$ is ______ MeV. [Take $m({}^{209}_{83}Bi)=208.980388$ u, $m_p=1.007825$ u, $m_n=1.008665$ u, 1 u = 931 MeV/c$^2$]

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom ______.

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, $\Delta Mc^2=$ ______ MeV.

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because A. The size of gold nucleus is very small as compared to the size of gold atom. B. Alpha particle and gold nucleus have equal charge. C. The impact parameter is minimum for a few alpha particles. D. A few alpha particles have very high kinetic energy. E. Only a few alpha particles undergo head-on collision with the nuclei. Choose the correct answer from the options given below:

In the hydrogen atom, the electron makes a transition from the higher orbit ($i$) to a lower orbit ($f$). The ratio of the radius of the orbits in given by $r_i : r_f = 16 : 4$. The wavelength of photon emitted due to this transition is ______nm. (Given Rydberg constant $= 1.0973 \times 10^7$ /m)

Assuming the experimental mass of $^{12}_{6}\mathrm{C}$ as 12 u, the mass defect of $^{12}_{6}\mathrm{C}$ atom is ______ MeV/$c^2$. (Mass of proton = 1.00727 u. mass of neutron = 1.00866 u, 1 u = 931.5 MeV/$c^2$ and $c$ is the speed of the light in vacuum).

The ratio of momentum of the photons of the $1^{\text{st}}$ and $2^{\text{nd}}$ line of Balmer series of Hydrogen atoms is $\alpha/\beta$. The possible values of $\alpha$ and $\beta$ are:-

The energy released when $\frac{7}{17.13}$ kg of $\mathrm{^7_3Li}$ is converted into $\mathrm{^4_2He}$ by proton bombardment is $\alpha\times10^{32}$ eV. The value of $\alpha$ is ____. (Nearest integer) (Mass of $\mathrm{^7_3Li}=7.0183$ u, mass of $\mathrm{^4_2He}=4.004$ u, mass of proton $=1.008$ u and 1 u $=931\ \mathrm{MeV/c^2}$ and Avogadro number $=6.0\times10^{23}$)

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same $Q$ value of 1 MeV. The ratio of energies of $\alpha$-rays produced by A and B is ______.