HARD
JEE Main
IMPORTANT
Earn 100

A Bi210 radionuclide decays via the chain,

Bi210λ1Po210λ2Pb206 stable

where, the decay constants are λ1=1.60×10-6 s-1, λ2=5.80×10-8 s-1. Calculate the alpha and beta-activities of the Bi210 preparation of the mass 1.00 mg a month after its manufacture.

Avogadro constant=6.023×1023 mol-1.

Important Questions on ATOMIC AND NUCLEAR PHYSICS

HARD
JEE Main
IMPORTANT
(a) What isotope is produced from the alpha-radioactive Ra226 (Z=88) as a result of five alpha-disintegrations and four β- disintegrations?
(b) How many alpha and β- decays does U238 (Z=92)  experience before turning finally into the stable Pb206 (Z=82)  isotope?
HARD
JEE Main
IMPORTANT

A stationary Pb200 nucleus emits an alpha-particle with kinetic energy Tα=5.77 MeV. Find the recoil velocity of the daughter nucleus. What fraction of the total energy liberated in this decay is accounted for by the recoil energy of the daughter nucleus?

mass of nucleons is 1.67×10-27 kg

HARD
JEE Main
IMPORTANT
Find the amount of heat generated by 1.00 mg of Po210 preparation during the mean lifetime period of these nuclei, if the emitted alpha-particles are known to possess the kinetic energy 5.3 MeVand practically all daughter nuclei are formed directly in the ground state.

Avogadro constant NA=6.023×1023 mol-1.

HARD
JEE Main
IMPORTANT
The alpha-decay of Po210 nuclei (in the ground state) is accompanied by the emission of two groups of alpha-particles with kinetic energies 5.30 and 4.50 MeV. Following the emission of these particles, the daughter nuclei are found in the ground and excited states. Find the energy of gamma-quanta emitted by the excited nuclei.
HARD
JEE Main
IMPORTANT
Find the energy Q liberated in β- and β+ decays and in K capture, if the masses of the parent atom Mp, the daughter atom Md and an electron m are known.( c is speed of light)
HARD
JEE Main
IMPORTANT
Taking the values of atomic masses from the tables, find the maximum kinetic energy of beta particles emitted by Be10 nuclei and the corresponding kinetic energy of the recoiling daughter nuclei formed directly in the ground state.

Be10=10.016711 amu
B10=10.016114 amu

HARD
JEE Main
IMPORTANT

Evaluate the amount of heat produced during a day by β- active Na24 preparation of mass m=1.0 mg. The beta-particles are assumed to possess an average kinetic energy equal to 1/3 of the highest possible energy of the given decay. The half-life of Na24 is T=15 hours.

Mass of Na24 is 24.00903 amu and of Mg24 is 24.01496 amu , energy equivalent of neutrinos or electron is 0.511 MeV

1 amu=1.67×10-24 g and 1 amu is equivalent to 931.5 MeV of energy, speed of light 3×108 ms-1.

HARD
JEE Main
IMPORTANT

Taking the values of the atomic masses from the tables, calculate the kinetic energies of a positron and a neutrino emitted by C11 nucleus for the case, when the daughter nucleus does not recoil.

Mass defect due to positron is 0.00213 amu, energy equivalent of neutrinos or electron is 0.511 MeV

1 amu=1.67×10-24 g and 1 amu is equivalent to 931.5 MeV of energy, speed of light 3×108 ms-1.