# Xam Idea Class 12 Physics Chapter 12 Solutions: Atoms

Xam Idea Class 12 Physics Solutions for Chapter 12 ‘Atoms’ give complete information on the properties of atoms. This book deals with the topic in detail, giving a lot of theoretical explanation along with questions which meet the needs of your CBSE exams and other prestigious competitive exams like IIT-JEE. Our Xam Idea solutions will help you learn the fundamentals of atoms and their composition along with the details of Geiger-Marsden’s α-particle Scattering Experiment. Atom’s anatomy is described by means of Rutherford’s Atom Model and Bohr’s model. You will also learn other concepts concerning atoms like impact parameter, the distance of closest approach, the energy of orbiting electrons, and the Hydrogen spectrum series.

Xam Idea Class 12 Physics Solutions Chapter 12 ‘Atoms’ has a total of 86 questions segregated into 8 sections. In these questions, you get to answer a variety of questions in different formats like short and long type answers, objective types, assertion-reason questions, and HOTS (high order thinking skills) problems. The questions take into account the difficulty level of the problems which come in actual exams. Many questions are taken from previous CBSE exams as well as some select NCERT questions are also there.

We, at Instasolv, strive to make the Xam Idea Physics problems look easy and comprehensible by solving each of them in detail. All the concepts behind a question are explained so that you are sure of how the derivations are done. Following our approach of tackling any question would give you enough confidence and you will not only get high scores in CBSE exams but also be able to assess your preparedness for competitive engineering and medical exams.

## Important Topics for Xam Idea Class 12 Physics Solutions Chapter 12: Atoms

**Atoms –**Atoms are small invisible particles present in all elements. They are in the shape of a sphere with a radius of 10^{-10}m.**Findings of the Geiger-Marsden’s α-particle Scattering Experiment –**In 1911 Rutherford’s associates Geiger and Marsden performed an experiment by bombarding α particles on a gold foil, and made these observations:

Most particles passed the foil undetected

A small number (1 in 8000) either suffered large-angle deflection or retraced their path by a 180º deflection

**Conclusions of the gold foil experiment:**

Atom is hollow with its entire positive charge and almost the whole mass is centred inside the nucleus

Negatively charged particles, electrons, are outside the nucleus.

One can apply Coulomb’s law for atomic distances

**Impact parameter –**When the α particles are far away, their velocity vector and the perpendicular distance from the nucleus is known as the impact parameter and given by:

B = (1/4πε_{0}) * (Ze^{2} * Cot(θ/2))/E_{K}

Here ε_{0} = permittivity of space = 8.854 x 10^{-12} C^{2} N^{-1} m^{-2}

θ – Angle of scattering – this is the angle by which α particles deviate from their original path

Z – Atomic number of the nucleus

e – Charge of the nucleus

** **E_{K}** – **initial kinetic energy for the head-on approach of α particle

**The distance of closest approach –**At a certain distance from the nucleus (r_{0}), the whole kinetic energy of α particles is converted into electrostatic potential energy and the particles can no longer move closer to the nucleus. This distance r_{0 }is called the distance of closest approach, which is a measure of the size of the nucleus. It is given by:

r** _{0 }**= (1/4πε

_{0}) * (2Ze

^{2}/E

_{K})

**Rutherford’s model of an atom –**According to Rutherford’s model, atoms have a heavy nucleus with positive charge while negative electrons are revolving around the nucleus. It could explain the neutrality of an atom, photoelectric effect, and thermionic emission. But it failed to explain the stability of an atom and also its line spectrum.**Bohr’s model of an atom –**Bohr modify Rutherford’s model to combine early quantum theory with the classical one and came up with 3 postulates:**Stationary circular orbit –**Electrons revolve around the nucleus in a stable orbit, without emitting radiant energy. These are called the stationary orbits. The necessary centripetal force is provided by the electrostatic Coulomb force between electrons and the nucleus:

mv^{2}/r = (1/4πε_{0}) * (Ze^{2} /r^{2})

**Quantum condition –**The angular momentum of electrons in these stationary orbits is a multiple of h/2π.

mvr = n * h/2π, here n = 1,2, 3, …. n

Here h – Planck’s constant = 6.6 * 10^{-34} J -s

This is the Bohr’s quantum condition and n is called the principal quantum number

**Transitions**– Transitions of electrons might happen from any of its stationary orbits to an orbit with lower energy. In that process, it emits or absorbs energy in the form of a photon whose energy is equal to the energy difference between the initial and final state. The frequency of the emitted photon is given by:

hv = E_{i} – E_{f,}, here E_{i} and E_{f, }are energies of initial and final states.

**Important formula related to Bohr’s model of an atom:**

Radii of stationary orbits r = n^{2}h^{2}/4π^{2}mkZe^{2}

The radius of the first orbit of H-atom is called Bohr’s radius, given by:

a_{0} = ε_{0}^{2}h^{2}/ πme^{2} = 0.529 * 10^{-10}

The velocity of electrons in Bohr’s stationary orbits:

v_{n} = e^{2}/2ε_{0}nh

Frequency of electrons in Bohr’s stationary orbits: Number of revolutions completed by an electron in its stationary orbit is its frequency and given by:

Ѵ = kZe^{2}/nhr

The total energy of an electron in stationary orbit:

En = – Rhc/n^{2} = – 13.6 ev/n^{2}

Here R is Rydberg’s constant = me^{4}/8 ε_{0}^{2}ch^{3}

### Discussion of Exercises of Xam Idea Class 12 Physics Solutions Chapter 12: Atoms

- There are 8 selected NCERT questions where you apply your knowledge on the gold foil experiment, calculate the frequency of energy radiated when electrons move from one orbit to another, find kinetic and potential energies of electrons.
- The 2
^{nd}set has 20 multiple-choice questions. There are some basic questions on properties of an atom, use of Bohr’s radius to calculate the radius of an electron in the ground state and problems on the hydrogen spectrum. - There is 1 assertion-reason type question in the 3
^{rd}10 statements with an assertion and its reason are given. One has to determine if either of them is correct or wrong. - The 4
^{th}set requires very short answers for its 10 questions. They include questions like Bohr’s radius in H-atom, radii ratio of the ground and first excited state of H-atom. - The 5
^{th}set has 18 questions that need short answers. Questions are based on:

- the distance of closest approach,
- explanation of limitations of the Rutherford model,
- plotting of graph for scattering angle and number of particles scattered in the gold foil experiment
- quantum number of the state when a photon in H-atom goes from ground state n to first excited state, given the work function and stopping potential

- The 6th set requires long answers for its 13 questions. There are questions on Bohr’s postulates, spectral lines of H-atom, and the muonic H-atom’s Bohr’s radius.
- The 7
^{th}set is again a long answer type with 3 questions. In the first question, you are given a choice to either describe the gold foil experiment or draw a schematic arrangement of that experiment. The 2^{nd}question has 3 choices to select from, 2 are on Bohr’s postulates and 1 is on the Rutherford model. In the 3rd question, you need to find the magnetic field due to revolving electrons in an H-atom. - In the 8
^{th}set, there are 13 questions where you can self assess your knowledge on the topics of this chapter. Questions encompass most of the key topics discussed.

## Why Use Xam Idea Class 12 Physics Solutions Chapter 12: Atoms by Instasolv?

- Atoms are an interesting topic in Physics but there are many theorems and formulas to memorize. Our academic experts will provide you with many strategies and tips on how to go over complicated problems and memorize the formulas easily.
- The Xam Idea Class 12 Physics Solutions are in line with the latest CBSE curriculum and you will surely get good grades in any exam you sit for. These free of cost solutions will also not bother you monetarily.