Atoms And Nuclei - Modern Physics - Physics Previous Year Questions

Consider that an electron is revolving in an excited state of Hydrogen atom with velocity $\sqrt{25.6} \times 10^5 \mathrm{~ms}^{-1}$. The radius of the orbit is $x \times 10^{-9} \mathrm{~m}$. The value of $x$ is:

[Take the mass of electron to the $9 \times 10^{-31} \mathrm{~kg}$, charge of electron $=-1.6 \times 10^{-19} \mathrm{C}$ and $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}$ ]

Consider the following nuclear reaction

$${ }^{238} \mathrm{U} \longrightarrow{ }^{234} \mathrm{Th}+{ }^4 \mathrm{He}$$

Take masses of ${ }^{238} \mathrm{U},{ }^{234} \mathrm{Th}$ and ${ }^4 \mathrm{He}$ as $238.050 \mathrm{u}, 234.043 \mathrm{u}$ and 4.003 u , respectively. The $Q$ value for the reaction, in keV, is:

[Given: $1 \mathrm{u}=931.5 \mathrm{MeV} \mathrm{c}^{-2}$ ]

In Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of scattering angle $\theta$. Which of the following options represents the correct plot?