Embibe Experts Solutions for Chapter: Structure of Atom, Exercise 1: JEE Advanced Paper 1 - 2013

Consider a helium $\left(\mathrm{He}\right)$ atom that absorbs a photon of wavelength $330 \mathrm{nm}$. The change in the velocity (in $\mathrm{cm} {\mathrm{s}}^{-1}$) of $\mathrm{He}$ atom after the photon absorption is ______.
(Assume: Momentum is conserved when a photon is absorbed.
Use: Planck constant $=6.6\times {10}^{-34} \mathrm{J} \mathrm{s}$, Avocados number $=6\times {10}^{23}{ \mathrm{mol}}^{-1}$, Molar mass of $\mathrm{He}=4 \mathrm{g}{ \mathrm{mol}}^{-1}$)

Give your answer as the nearest integer.

In an experiment, $\mathrm{m}$ grams of a compound $\mathrm{X}$ (gas/liquid/solid) taken in a container is loaded in a balance as shown in figure $\mathrm{I}$ below. In the presence of a magnetic field, the pan with $\mathrm{X}$ is either deflected upwards (figure $\mathrm{II}$), or deflected downwards (figure $\mathrm{III}$), depending on the compound $\mathrm{X}$. Identify the correct statement(s).

The figure below is the plot of potential energy versus internuclear distance $\left(\mathrm{d}\right)$ of ${\mathrm{H}}_2$ molecule in the electronic ground state. The value of the net potential energy ${\mathrm{E}}_0$ (as indicated in the figure) is $-5.24649\times {10}^{\mathrm{n}}$ $\mathrm{kJ} {\mathrm{mol}}^{-1},$ for $\mathrm{d}={\mathrm{d}}_0$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent, find the value of $\mathrm{n}$ to the nearest integer value.

As reference, the potential energy of $\mathrm{H}$ atom is taken as zero when its electron and the nucleus are infinitely far apart.

Use Avogadro constant as $6.023\times {10}^{23} {\mathrm{mol}}^{-1}.$  Give an answer to the nearest integer value.

The ground state energy of hydrogen atom is $-13.6\mathrm{ }\mathrm{e}\mathrm{V}$ . Consider an electronic state $\mathrm{\Psi }$ of ${\mathrm{H}\mathrm{e}}^{+}$ whose energy, azimuthal quantum number and magnetic quantum number are $-3.4\mathrm{ }\mathrm{e}\mathrm{V},\mathrm{ }2$ and $0$ respectively. Which of the following statement(s) is(are) true for the state $\mathrm{\Psi }$ ?

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\mathrm{t}\mathrm{h}}$ orbit of the atom and List-II contains options showing how they depend on $n$ .
 

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\mathrm{t}\mathrm{h}}$ orbit of the atom and List-II contains options showing how they depend on $n$ .
 

Among the species given below, the total number of diamagnetic species is ___.

$H \mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}, N{O}_2 \mathrm{m}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}, O_2^{-}$ (superoxide), dimeric sulphur in vapour phase, ${\mathrm{Mn}}_3{\mathrm{O}}_4,\mathrm{ }{\left({\mathrm{NH}}_4\right)}_2\left[{\mathrm{FeCl}}_4\right],\mathrm{ }{\left({\mathrm{NH}}_4\right)}_2\left[{\mathrm{NiCl}}_4\right],\mathrm{ }{\mathrm{K}}_2{\mathrm{MnO}}_4,\mathrm{ }{\mathrm{K}}_2{\mathrm{CrO}}_4$

The wave function, ${\mathrm{\psi }}_{\mathrm{n}}$ is a mathematical function whose value depends upon spherical polar coordinates $\left(\mathrm{r},\mathrm{ }\mathrm{\theta },\mathrm{ }\mathrm{\varphi }\right)$ of the electron and characterized by the quantum numbers $\mathrm{n},\mathrm{ }\mathrm{l}$ and ${\mathrm{m}}_{\mathrm{l}}$ . Here $\mathrm{r}$ is the distance from the nucleus, $\mathrm{\theta }$ is colatitude and $\mathrm{\varphi }$ is azimuth. In the mathematical functions given in the Table, $\mathrm{Z}$is the atomic number and ${\mathrm{a}}_{\mathrm{o}}$ is Bohr radius