Embibe Experts Solutions for Chapter: Atoms and Nuclei, Exercise 1: JEE Main - 12th January 2019 Shift 2

A radioactive nucleus decays by two different process. The half life of the first process is $5$ minutes and that of the second process is $30 \mathrm{s}$. The effective half-life of the nucleus is calculated to be $\frac{\alpha }{11} \mathrm{s}$. The value of $\alpha$ is ______.

For hydrogen atom, ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths corresponding to the transitions $1$ and $2$ respectively as shown in figure. The ratio of ${\lambda }_1$ and ${\lambda }_2$ is $\frac{x}{32}$. The value of $x$ is ______.

The radius of electron's second stationary orbit in Bohr's atom is $R$. The radius of $3^{rd}$ orbit will be

If the binding energy of ground state electron in a hydrogen atom is $13.6 \mathrm{eV}$, then, the energy required to remove the electron from the second excited state of $\mathrm{Li}{ }^{2+}$ will be: $x\times {10}^{-1} \mathrm{eV}$. The value of $x$ is _____.

The mass of proton, neutron and helium nucleus are respectively $1.0073 \mathrm{u}, 1.0087 \mathrm{u} \mathrm{and} 4.0015\mathrm{u}$. The binding energy of helium nucleus is:

A light of energy $12.75 \mathrm{eV}$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi }\times {10}^{-17} \mathrm{eVs}$. The value of $x$ is ______ (use $h=4.14\times {10}^{–15} \mathrm{eVs}, c=3 \times {10}^8 \mathrm{m} {\mathrm{s}}^{–1}$)

An electron of a hydrogen like atom, having $Z = 4$, jumps from $4^{th}$ energy state to $2^{nd}$ energy state, The energy released in this process, will be: (Given $Rch = 13.6 eV$)

Where $R =$ Rydberg

constant $c =$Speed of light in vacuum

$h =$ Planck's constant

Nucleus $A$ having $Z=17$ and equal number of protons and neutrons has $1.2 \mathrm{MeV}$ binding energy per nucleon. Another nucleus $B$ of $Z=12$ has total $26$ nucleons and $1.8 \mathrm{MeV}$ binding energy per nucleons. The difference of binding energy of $B$ and $A$ will be ______ $\mathrm{MeV}$.