Physics · Class 12 Science
Ch 12Atoms — Class 12 Physics, concept-first.
By the close of the nineteenth century, enough experimental evidence had built up in favour of the atomic hypothesis of matter — the idea that all matter is made up of tiny, indivisible particles called atoms. A crucial breakthrough came in 1897, when the English physicist J. J.
Key concepts
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Scale Analogy
Rutherford's gold-foil experiment revealed something almost impossible to picture: the atom's entire positive charge and nearly all of its mass sit inside a nucleus that is fantastically smaller than the atom around it.
Most relevant Q&A
- In the Rutherford's nuclear model of the atom, the nucleus (radius about $10^{-15}\ \text{m}$) is analogous to the sun about which the elect…Free
- Choose the correct alternative from the clues given at the end of each statement: (a) The size of the atom in Thomson's model is ..........…Free
- Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not…Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
By the close of the nineteenth century, enough experimental evidence had built up in favour of the atomic hypothesis of matter — the idea that all matter is made up of tiny, indivisible particles call…
Alpha-particle Scattering and Rutherford's Nuclear Model of Atom
In 1911, at Rutherford's suggestion, Geiger and Marsden performed a landmark experiment. They directed a beam of 5.5 MeV alpha-particles from a radioactive source (Bi) at a very thin gold foil of thic…
Alpha-particle Trajectory
When a beam of alpha particles is fired at a thin gold foil, each particle follows a curved path — a trajectory — determined by the repulsive electric force from the nucleus.
+−Worked Examplesi2 questions
- Example 12.1In the Rutherford's nuclear model of the atom, the nucleus (radius about $10^{-15}\ \text{m}$) is analogous to the sun about which the elect…Free
- Example 12.2In a Geiger-Marsden experiment, what is the distance of closest approach to the nucleus of a $7.7\ \text{MeV}$ $\alpha$-particle before it c…Preview
Electron Orbits
In Rutherford's nuclear model, the atom is visualised as a tiny, massive, positively charged nucleus surrounded by electrons that revolve around it in well-defined orbits.
Atomic Spectra
The story of atomic spectra begins with a simple observation that shattered classical physics. When hydrogen gas is heated or electrically excited, it does not emit a continuous rainbow of colours.
Bohr Model of the Hydrogen Atom
Rutherford's nuclear model — a tiny positive nucleus with electrons orbiting around it — seemed plausible at first glance.
Energy Levels
The energy of an atom is not a continuous quantity — it takes only certain discrete values. For a hydrogen atom, the energy is most negative (i.e., the lowest) when the electron is in the orbit closes…
The Line Spectra of the Hydrogen Atom
When an electron in a hydrogen atom jumps from a higher energy level (quantum number ) to a lower one (, where ), the atom loses energy.
De Broglie's Explanation of Bohr's Second Postulate of Quantisation
Bohr's second postulate — that the angular momentum of an orbiting electron is quantised as — was a brilliant guess that worked, but it had no physical justification within Bohr's own model.
Summary
- Rutherford’s -particle scattering experiment showed that the atom has a tiny, dense, positively charged nucleus, with electrons orbiting at large distances — most of the atom is empty space.
Points to Ponder
1. Both Thomson's and Rutherford's atomic models turn out to be unstable, just for different reasons. Thomson's positively-charged "cloud" model is electrostatically unstable; Rutherford's nuclear mod…
Exercises
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- 12.1Choose the correct alternative from the clues given at the end of each statement: (a) The size of the atom in Thomson's model is ..........…Free
- 12.2Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold…Free
- 12.4What is the shortest wavelength present in the Paschen series of spectral lines?Free
- 12.5A difference of $2.3\ \text{eV}$ separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a tr…Preview
- 12.6The ground state energy of hydrogen atom is $-13.6\ \text{eV}$. What are the kinetic and potential energies of the electron in this state?Preview
- 12.7A hydrogen atom initially in the ground level absorbs a photon, which excites it to the $n = 4$ level. Determine the wavelength and frequenc…Preview
- 12.8(a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the $n = 1, 2,$ and $3$ levels. (b) Calculate the orbit…Preview
- 12.9The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11}\ \text{m}$. What are the radii of the $n = 2$ and $n =…Preview
- 12.10A $12.5\ \text{eV}$ electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?Preview
- 12.10In accordance with the Bohr's model, find the quantum number that characterises the earth's revolution around the sun in an orbit of radius…Preview
Additional Exercises
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- 12.11Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better. (a) Is the a…Free
- 12.12The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about $10^{…Free
- 12.13Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level $n$ to level $(n-1)$. For large $n$,…Free
- 12.14Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not…Preview
- 12.15The total energy of an electron in the first excited state of the hydrogen atom is about $-3.4\ \text{eV}$. (a) What is the kinetic energy o…Preview
- 12.16If Bohr's quantisation postulate (angular momentum $= nh/2\pi$) is a basic law of nature, it should be equally valid for the case of planeta…Preview
- 12.17Obtain the first Bohr's radius and the ground state energy of a muonic hydrogen atom [i.e., an atom in which a negatively charged muon ($\mu…Preview
NCERT Exemplar
Higher-order thinking problems from the NCERT Exemplar.
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- Q1Taking the Bohr radius as $a_0 = 53\ \text{pm}$, the radius of $\text{Li}^{++}$ ion in its ground state, on the basis of Bohr's model, will…Free
- Q2The binding energy of a H-atom, considering an electron moving around a fixed nucleus (proton), is $B = -\dfrac{m e^4}{8 n^2 \varepsilon_0^2…Free
- Q3The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because (a) of the e…Free
- Q4For the ground state, the electron in the H-atom has an angular momentum $= \dfrac{h}{2\pi}$, according to the simple Bohr model. Angular mo…Preview
- Q5$\text{O}_2$ molecule consists of two oxygen atoms. In the molecule, nuclear force between the nuclei of the two atoms (a) is not important…Preview
- Q6Two H atoms in the ground state collide inelastically. The maximum amount by which their combined kinetic energy is reduced is (a) $10.20\ \…Preview
- Q7A set of atoms in an excited state decays. (a) in general to any of the states with lower energy. (b) into a lower state only when excited b…Preview
- Q8The mass of a H-atom is less than the sum of the masses of a proton and electron. Why is this?Preview
- Q9Imagine removing one electron from $\text{He}^4$ and $\text{He}^3$. Their energy levels, as worked out on the basis of Bohr model will be ve…Preview
- Q10When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic r…Preview
- Q11Would the Bohr formula for the H-atom remain unchanged if proton had a charge $(+4/3)e$ and electron a charge $(-3/4)e$, where $e = 1.6 \tim…Preview
- Q12Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different…Preview
- Q13Positronium is just like a H-atom with the proton replaced by the positively charged anti-particle of the electron (called the positron whic…Preview
- Q14Assume that there is no repulsive force between the electrons in an atom but the force between positive and negative charges is given by Cou…Preview
- Q15Using Bohr model, calculate the electric current created by the electron when the H-atom is in the ground state.Preview
- Q16Show that the first few frequencies of light that is emitted when electrons fall to the $n$th level from levels higher than $n$, are approxi…Preview
- Q17What is the minimum energy that must be given to a H atom in ground state so that it can emit an $H_\gamma$ line in Balmer series? If the an…Preview
- Q18The first four spectral lines in the Lyman series of a H-atom are $\lambda = 1218\ \text{\AA}, 1028\ \text{\AA}, 974.3\ \text{\AA}$ and $951…Preview
- Q19Deuterium was discovered in 1932 by Harold Urey by measuring the small change in wavelength for a particular transition in $^1\text{H}$ and…Preview
- Q20If a proton had a radius $R$ and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when…Preview
- Q21In the Auger process an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer ele…Preview
- Q22The inverse square law in electrostatics is $|\vec{F}| = \dfrac{e^2}{4\pi\varepsilon_0 r^2}$ for the force between an electron and a proton.…Preview
- Q23The Bohr model for the H-atom relies on the Coulomb's law of electrostatics. Coulomb's law has not directly been verified for very short dis…Preview
- Q24An ionised H-molecule consists of an electron and two protons. The protons are separated by a small distance of the order of angstrom. In th…Preview
- Q25Consider aiming a beam of free electrons towards free protons. When they scatter, an electron and a proton cannot combine to produce a H-ato…Preview
- Q26The Bohr model for the spectra of a H-atom (a) will not be applicable to hydrogen in the molecular form. (b) will not be applicable as it is…Preview
- Q27The Balmer series for the H-atom can be observed (a) if we measure the frequencies of light emitted when an excited atom falls to the ground…Preview
- Q28Let $E_n = -\dfrac{m e^4}{8 n^2 \varepsilon_0^2 h^2}$ be the energy of the $n$th level of H-atom. If all the H-atoms are in the ground state…Preview
- Q29The simple Bohr model is not applicable to $\text{He}^4$ atom because (a) $\text{He}^4$ is an inert gas. (b) $\text{He}^4$ has neutrons in t…Preview
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