In a radioactive decay chain reaction, ${ }_{90}^{230} Th$ nucleus decays into ${ }_{84}^{214} Po$ nucleus. The ratio of the number of $\alpha$ to number of $\beta^{-}$particles emitted in this process is. . . . . 

  • [IIT 2022]
  • A

    $4$

  • B

    $2$

  • C

    $3$

  • D

    $8$

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The half-life of a radioactive substance is $3.6$ days. How much of $20\, mg$ of this radioactive substance will remain after $36$ days ............. $mg$

Radioactive substances do not emit

Match the nuclear processes given in column $I$ with the appropriate option$(s)$ in column $II$

column $I$ column $II$
$(A.)$Nuclear fusion $(P.)$ Absorption of thermal neutrons by ${ }_{92}^{213} U$
$(B.)$Fission in a nuclear reactor $(Q.)$ ${ }_{27}^{60} Co$ nucleus
$(C.)$ $\beta$-decay $(R.)$ Energy production in stars via hydrogen conversion to helium
$(D.)$ $\gamma$-ray emission $(S.)$ Heavy water
  $(T.)$ Neutrino emission

  • [IIT 2015]

The half-life of ${ }^{198} {Au}$ is $3 \,days.$ If atomic weight of ${ }^{198} {Au}$ is $198\, {g} / {mol}$ then the activity of $2 \,{mg}$ of ${ }^{198} {Au}$ is ..... $\times 10^{12}\,disintegration/second$

  • [JEE MAIN 2021]