Nuclei

13.1 (a) Two stable isotopes of lithium ${}_3{}^6\mathit{L}\mathit{i}$ and ${}_3{}^7\mathit{L}\mathit{i}$ have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.

(b) Boron has two stable isotopes, ${}_5{}^{10}\mathit{B}$ and ${}_5{}^{11}\mathit{B}$ . Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of ${}_5{}^{10}\mathit{B}$ and ${}_5{}^{11}\mathit{B}$ 10.

The variation of decay rate of two radioactive samples A and B with time is shown in figure.

Which of the following statements are true?

(a) Decay constant of A is greater thanB, hence A is always decays faster than B

(b) Decay constant of B is greater than that of A but its decay rate is smaller than that of A

(c) Decay constant of A is greater than that og B but it is does not always faster than B

(d) Decay constant of B is smaller than that of A but still decay rate becomes equal to that of A at later instant

Samples of two radioactive nuclides A and B are taken. λ_Aand λ_B are the disintegration constants of A and B respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?
(a) Initial rate of decay of A is twice the initial rate of decay of B and λ_A = λ_B
(b) Initial rate of decay of A is twice the initial rate of decay of B and λ_A > λ_B
(c) Initial rate of decay of B is twice the initial rate of decay of A and  λ_A > λ_B
(d) Initial rate of decay of B is same as the rate of decay of A at t = 2h and  λ_A < _B

Fusion processes, like combining two deuterons to form a He nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact 
(a) Nuclear forces have short range
(b) Nuclei are positively charged
(c) The original nuclei must be completely ionized before fusion can take place
(d) The original nuclei must first break up before combining with each other

In a nuclear reactor, moderators slow down the neutrons which come out in a fission process. The moderator used have light nuclei. Heavy nuclei will not serve the purpose, because
(a) They will break up
(b) Elastic collision of neutrons with heavy nuclei will not slow them down
(c) The net weight of the reactor would be unbearably high
(d) Substances with heavy nuclei do not occur in liquid or gaseous state at room temperature

Heavy stable nuclei have more neutrons than protons. This is because of the fact that .

(a) Neutrons are heavier than protons
(b) Electrostatic force between protons are repulsive
(c) Neutrons decay into protons through beta decay
(d) Nuclear forces between neutrons are weaker than that between protons

Tritium is an isotope of hydrogen whose nucleus triton contains 2 neutrons and 1 proton. Free neutrons decay into p + e + n . If one of the neutrons in Triton decays, it would transform into He³ nucleus. This does not happen. This is because
(a) Triton energy is less than that of a He³ nucleus
(b) The electron created in the beta decay process cannot remain in the nucleus
(c) Both the neutrons in triton have to decay simultaneously resulting in a nucleus with 3 protons, which is not a He³ nucleus.
(d) Free neutrons decay due to external perturbations which is absent in triton nucleus

M_e and M_s denote the atomic masses of the parent and he daughter nuclei respectively in radioactive decay. The Q value for a beta^-1 decay is Q₁ and that for beta+ decay is Q₂.if m_e denotes the mass of an electron, then which of the following statements is correct?

(a) Q₁=(M_x-M_y)c² and Q₂=[M_x-M_y-2m_e]c²

(b) Q₁=(M_x-M_y)c² and Q₂=[M_x-M_y]c²

(c) Q₁=(M_x-M_y-2m_e)c² and Q₂=[M_x-M_y-2C_e]c²

(d) Q₁=(M_x-M_y +2m_e)c² and Q₂=[M_x-M_y+2m_e]c²

When a nucleus in an atom undergoes a radioactive decay, the electronic energy levels of the atom
(a) Do not change for any type of radioactivity
(b) Change for α and β-radioactivity but not for γ-radioactivity
(c) Change for α -radioactivity but not for others
(d) Change for β-radioactivity but not for others

The gravitational force between a H atom and a another particle of mass m will be given newton's law

F=GMm/r² where r in km

(a) M=m_proton+m_electron

(b) M=m_proton+m_electron-

(c) M is not relate to the mass of the hydrogen atom

(d) M=m_proton+m_electron-(|V|)= magnitude of the potential energy of electron in H atom.