Dual Nature, Atoms & Nuclei · JEE Advanced previous year questions

2023 3 questions

1. Q252023 · 4 Jun 2023 · Paper 1· Numerical answer

   A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to level $n=3$ in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is $1.95\mathrm{eV}$. If the photoelectric threshold wavelength for the target metal is $310\mathrm{nm}$, the value of $Z$ is ____. [Given: $hc=1240\mathrm{eV}\text{-}\mathrm{nm}$ and $Rhc=13.6\mathrm{eV}$, where $R$ is the Rydberg constant, $h$ is the Planck's constant and $c$ is the speed of light in vacuum]

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   Answer: 3

2. Q312023 · 4 Jun 2023 · Paper 1

   List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. $$\begin{array}{ll}\text{List-I}& \text{List-II}\\ \text{(P) }{}_{92}^{238}\mathrm{U}\to {}_{91}^{234}\mathrm{Pa}& \text{(1) one }\alpha \text{ particle and one }{\beta }^{+}\text{ particle}\\ \text{(Q) }{}_{82}^{214}\mathrm{Pb}\to {}_{82}^{210}\mathrm{Pb}& \text{(2) three }{\beta }^{-}\text{ particles and one }\alpha \text{ particle}\\ \text{(R) }{}_{81}^{210}\mathrm{Tl}\to {}_{82}^{206}\mathrm{Pb}& \text{(3) two }{\beta }^{-}\text{ particles and one }\alpha \text{ particle}\\ \text{(S) }{}_{91}^{228}\mathrm{Pa}\to {}_{88}^{224}\mathrm{Ra}& \text{(4) one }\alpha \text{ particle and one }{\beta }^{-}\text{ particle}\\ & \text{(5) one }\alpha \text{ particle and two }{\beta }^{+}\text{ particles}\end{array}$$

   1. A.$P\to 4,Q\to 3,R\to 2,S\to 1$
   2. B.$P\to 4,Q\to 1,R\to 2,S\to 5$
   3. C.$P\to 5,Q\to 3,R\to 1,S\to 4$
   4. D.$P\to 5,Q\to 1,R\to 3,S\to 2$
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   Answer: A

3. Q292023 · 4 Jun 2023 · Paper 2· Numerical answer

   In a radioactive decay process, the activity is defined as $A=-\frac{dN}{dt}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources, $S_1$ and $S_2$ have same activity at time $t=0$. At a later time, the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$, respectively. When $S_1$ and $S_2$ have just completed their $3^{\mathrm{rd}}$ and $7^{\mathrm{th}}$ half-lives, respectively, the ratio $A_1/A_2$ is ____.

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   Answer: 16