If  the  half  lives  of  a  radioactive  element  for  $\mathrm{\alpha }$  and  β  decay  are  4  years  and  12  years  respectively,  the  ratio  of  its  initial  activity  and  that  after  12  years will be

• 6.25 %

• 12.5 %

• 25 %

• 50 %

232.

A radioactive nucleus is being produced  at  a constant  rate  $\mathrm{\alpha }$  per  second. Its  decay  constant  is  λ. If N₀ are the  number  of  nuclei  at  time  t = 0, then the maximum number of  nuclei possible are

• N₀  +  $\frac{\mathrm{\alpha }}{\mathrm{\lambda }}$

• N₀

• $\frac{\mathrm{\lambda }}{\mathrm{\alpha }}$ + N₀

• $\frac{\mathrm{\alpha }}{\mathrm{\lambda }}$

Assertion: Nuclei  having mass  number  about  60 are  most stable. 

Reason:  When  two  or  more  light  nuclei  are  combined  into  a  heavier  nucleus, then the binding  energy  per  nucleon  will increase.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

N₁ atoms of a radioactive element emit N₂ beta particles per second. The decay constant of the element is ( m s^-1 )

• N₁/N₂

• N₂/N₁

• N₁ ( ln2 )

• N₂ ( ln2 )

Assertion:  ⁹⁰Sr from the radioactive fall out from a nuclear bomb ends up in the bones of human beings through the milk consumed by them. It causes impairment of production of red blood cells.

Reason: The energies β-particles emitted in the decay of  ⁹⁰Sr damage the bone marrow.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

What is the amount of energy released by deuterium and tritium fusion?  [ Given: ${\mathrm{M}}_{{}_1{}^2\mathrm{H}}$ =2.0141024 u,  ${\mathrm{M}}_{{}_1{}^3\mathrm{H}}$ = 3.0160504 ,  ${\mathrm{M}}_{{}_0{}^1\mathrm{n}}$ = 1.0086654 u ]

• 60.6 eV

• 12.6 eV

• 17.6 eV

• 28.3 eV

What is the energy of photon whose wavelength is 6840 $\stackrel{\circ }{\mathrm{A}}$ ?

• 1.81 eV

• 3.6 eV

• $-$ 13.6 eV

• 12.1 eV

Calculate power output of  ${}_{92}{}^{235}\mathrm{U}$ reactor, if it is takes 30 days to use up 2 kg of fuel, and if each fission gives  185 MeV of useable energy. Avogadro's number = 6 × 10²³ / mol?

• 56.3 MW

• 60.3 MW

• 58.3 MW

• 54.3 MW

Assertion: Heavy water is a better moderator than normal water.

Reason: Heavy water absorbs neutrons more efficiently than normal water.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion:  ⁹⁴Sr from the radioactive fall out from a nuclear bomb ends up in the bones of human beings through the milk consumed by them. It causes impairment of the production of red blood cells. 

Reason: The energetics  β-particles emitted in the decay of  ⁹⁴Sr damage the bone marrow.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false