Physics · Class 12 Science
Ch 15Structure of Atoms and Nuclei — Class 12 Physics, concept-first.
The idea that matter is built from tiny, indivisible pieces goes back to the Greek philosophers Leucippus and Democritus in the 5th century BC, who first proposed 'atoms' -- literally 'uncuttable' -- as the ultimate building blocks of matter.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Bohr Model — Energy Levels, Ionization and Excitation Energy
Combining the orbit-radius and orbital-speed formulas with the definition of total energy (kinetic plus electrostatic potential) gives the central result of Bohr's model: the energy of an electron in the nth orbit of a h…
Most relevant Q&A
- State the postulates of Bohr's atomic model and derive the expression for the energy of an electron in the atom.Free
- Define excitation energy, binding energy and ionization energy of an electron in an atom.Preview
- Energy of an electron in the second Bohr orbit is –3.4 eV. Calculate the energy of an electron in the third Bohr orbit.Preview
- What is binding energy of a hydrogen atom?Preview
- Energy of an electron in second Bohr orbit is −3.4 eV. Calculate its kinetic energy and potential energy in third Bohr orbit.Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
The idea that matter is built from tiny, indivisible pieces goes back to the Greek philosophers Leucippus and Democritus in the 5th century BC, who first proposed 'atoms' -- literally 'uncuttable' --…
Thomson's Atomic Model
J.J. Thomson's discovery of the electron came from studying the rays produced inside an evacuated glass tube when a high voltage was applied between two electrodes.
Geiger-Marsden Experiment
To probe how an atom's positive charge is actually distributed, Rutherford proposed bombarding atoms with alpha particles -- positively charged particles (each carrying a charge of +2e, equal to that…
Rutherford's Atomic Model
Rutherford reasoned carefully from the Geiger-Marsden results. In Thomson's plum-pudding model, the positive charge is spread over a sphere the size of the whole atom, so its charge density is very lo…
Difficulties with Rutherford's Model
Elegant as it was at explaining the scattering data, Rutherford's model ran into a serious theoretical problem the moment classical physics was applied to it rigorously.
Atomic Spectra
When an ordinary solid object is heated, it glows and emits light across a broad, continuous range of wavelengths -- passing that light through a prism produces a smooth, unbroken rainbow (a continuou…
Bohr's Atomic Model
Niels Bohr resolved the contradiction between Rutherford's mostly-correct nuclear picture and the classical prediction of atomic collapse by borrowing ideas from the newly emerging quantum physics of…
Radii of the Orbits
Bohr's first two postulates together are enough to work out the size of each allowed orbit. Let the electron (mass ) move with speed in a circular orbit of radius , the nth stable orbit.
Energy of the Electrons
The electron's total energy in the nth orbit is the sum of its kinetic energy and its (negative) electrostatic potential energy, .
Limitations of Bohr's Model
Bohr's model was a triumph for hydrogen, but it had real limits. First and most seriously, it could not explain the spectral lines of any atom OTHER than hydrogen (or other single-electron, hydrogen-l…
De Broglie's Explanation
Chapter 14 established that matter, not just light, has a dual wave-particle nature: every material particle has an associated wave, with wavelength given by the de Broglie relation .
Atomic Nucleus
Having built up a working picture of how electrons are arranged and behave around the nucleus, the chapter now turns to the nucleus itself.
Constituents of a Nucleus
The atomic nucleus is built from two types of subatomic particles, together called nucleons: protons and neutrons.
Sizes of Nuclei
Just as different atoms have different overall sizes depending on how many electron orbits they occupy, different nuclei have different sizes depending on how many nucleons they contain.
Nuclear Forces
Physics recognises four fundamental forces of nature, and the one responsible for holding the nucleus together -- overcoming the mutual electrostatic repulsion between its positively charged protons -…
Nuclear Binding Energy
Section 15.7.1's list of proton and neutron masses can be used to check a striking fact: the actual measured mass of any real nucleus is always slightly LESS than the sum of the masses its individual…
Radioactive Decays
Most naturally occurring nuclei are perfectly stable, remaining unchanged indefinitely. But many others are not: they spontaneously transform, emitting some particle in the process and changing into a…
Law of Radioactive Decay
Even though an individual radioactive nucleus's decay is intrinsically unpredictable -- there is no way to say in advance exactly when any ONE particular nucleus will decay -- the behaviour of a large…
Half-life of Radioactive Material
The half-life of a radioactive species, denoted , is defined as the time required for the number of parent nuclei to fall to exactly HALF its initial value.
Average Life of a Radioactive Species
Different individual nuclei of the very same radioactive species do not all decay at the same moment -- some decay almost immediately, others survive for a very long time -- so it is natural to ask fo…
Nuclear Energy
Everyday energy sources -- fossil fuels such as coal, petroleum and natural gas, along with firewood -- release energy through CHEMICAL reactions, typically involving only a few electron-volts (eV) of…
Nuclear Fission
Nuclear fission exploits the DECREASING part of the binding-energy curve (Fig.15.6) on its heavy-nucleus side: a very heavy nucleus, with mass number around A = 230, has a lower binding energy per nuc…
Nuclear Fusion
Nuclear fusion exploits the OTHER, rising part of the binding-energy curve (Fig.15.6), on its light-nucleus side: light nuclei (with mass number below about A = 40) have a lower binding energy per nuc…
Long Answer Questions
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- Q11State the postulates of Bohr's atomic model and derive the expression for the energy of an electron in the atom.Free
- Q12Starting from the formula for energy of an electron in the nth orbit of hydrogen atom, derive the formula for the wavelengths of Lyman and B…Free
- Q13Determine the maximum angular speed of an electron moving in a stable orbit around the nucleus of hydrogen atom.Free
- Q14Determine the series limit of Balmer, Paschen and Brackett series, given the limit for Lyman series is 911.6 Å.Preview
- Q15Describe alpha, beta and gamma decays and write down the formulae for the energies generated in each of these decays.Preview
- Q16Explain what are nuclear fission and fusion giving an example of each. Write down the formulae for energy generated in each of these process…Preview
- Q17Describe the principles of a nuclear reactor. What is the difference between a nuclear reactor and a nuclear bomb?Preview
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
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- Q1The decay constant of a radioactive substance is $4.33\times10^{-4}$ per year. Calculate its half life period.Preview
- Q2Find the frequency of revolution of an electron in Bohr's 2nd orbit; if the radius and speed of electron in that orbit is $2.14\times10^{-10…Preview
- Q3An electron in an atom revolves around the nucleus in an orbit of radius 0.53 Å. If the frequency of revolution of an electron is $9\times10…Preview
- Q4The electron in the hydrogen atom is moving with a speed of $2.3 \times 10^6$ m/s in an orbit of radius 0.53 Å. Calculate the period of revo…Preview
- Q5Using an expression for energy of electron, obtain the Bohr's formula for hydrogen spectral lines. **OR** State the law of radioactive decay…Preview
- Q6In hydrogen atom, electron jumps from the 3rd orbit to the 1st orbit. The change in angular momentum is _______. (A) $1.05 \times 10^{-34}$…Preview
- Q7State the name of the visible series in hydrogen spectrum.Preview
- Q8State any two postulates of Bohr's theory of hydrogen atom.Preview
- Q9Energy of an electron in the second Bohr orbit is –3.4 eV. Calculate the energy of an electron in the third Bohr orbit.Preview
- Q10What is the mathematical formula for third postulate of Bohr's atomic model?Preview
- Q11Derive an expression for the radius of the $n^{th}$ Bohr orbit of the electron in hydrogen atom.Preview
- Q12An electron in an atom is revolving round the nucleus in a circular orbit of radius $5.3 \times 10^{-11}$ m with a speed of $3 \times 10^6$…Preview
- Q13Determine the shortest wavelengths of Balmer and Paschen series. Given the limit for Lyman series is 912 Å.Preview
- Q14The radius of eighth orbit of electron in H-atom will be more than that of fourth orbit by a factor of ______. (a) 2 (b) 4 (c) 8 (d) 16Preview
- Q15Write the mathematical formula for Bohr magneton for an electron revolving in $n^{th}$ orbit.Preview
- Q16Disintegration rate of a radio-active sample is $10^{10}$ per hour at 20 hours from the start. It reduces to $5 \times 10^{9}$ per hour afte…Preview
- Q17State postulates of Bohr's atomic model.Preview
- Q18What is binding energy of a hydrogen atom?Preview
- Q19Calculate the change in angular momentum of electron when it jumps from third orbit to first orbit in hydrogen atom.Preview
- Q20Calculate the wavelength of the first two lines in Balmer series of hydrogen atom.Preview
- Q21Derive an expression for law of radioactive decay. Define one becquerel (Bq).Preview
- Q22An electron in hydrogen atom stays in its second orbit for 10⁻⁸ s. How many revolutions will it make around the nucleus in that time? [Given…Preview
- Q23What is beta plus decay?Preview
- Q24Derive an expression for radius of nth Bohr orbit.Preview
- Q25Energy of an electron in second Bohr orbit is −3.4 eV. Calculate its kinetic energy and potential energy in third Bohr orbit.Preview
More questions
25 Q+−Show 5 questionsHide questions5 questions
- Q6State the postulates of Bohr's atomic model.Free
- Q7State the difficulties faced by Rutherford's atomic model.Free
- Q8What are alpha, beta and gamma decays?Preview
- Q9Define excitation energy, binding energy and ionization energy of an electron in an atom.Preview
- Q10Show that the frequency of the first line in Lyman series is equal to the difference between the limiting frequencies of Lyman and Balmer se…Preview
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- Q1In which of the following systems will the radius of the first orbit of the electron be smallest? (A) hydrogen (B) singly ionized helium (C)…Free
- Q2The radius of the 4th orbit of the electron will be smaller than its 8th orbit by a factor of (A) 2 (B) 4 (C) 8 (D) 16Free
- Q3In the spectrum of hydrogen atom which transition will yield longest wavelength? (A) n = 2 to n = 1 (B) n = 5 to n = 4 (C) n = 7 to n = 6 (D…Preview
- Q4Which of the following properties of a nucleus does not depend on its mass number? (A) radius (B) mass (C) volume (D) densityPreview
- Q5If the number of nuclei in a radioactive sample at a given time is N, what will be the number at the end of two half-lives? (A) N/2 (B) N/4…Preview
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- Q18Calculate the binding energy of an alpha particle given its mass to be 4.00151 u.Free
- Q19An electron in hydrogen atom stays in its second orbit for $10^{-8}$ s. How many revolutions will it make around the nucleus in that time?Free
- Q20Determine the binding energy per nucleon of the americium isotope $_{95}^{244}$Am, given the mass of $_{95}^{244}$Am to be 244.06428 u.Free
- Q21Calculate the energy released in the nuclear reaction $_3^7$Li + p $\rightarrow$ 2 $_2^4$He given the mass of $_3^7$Li atom and of helium at…Preview
- Q22Complete the following equations describing nuclear decays. (a) $_{88}^{226}$Ra $\rightarrow$ ____ + $_2^4$He (b) $_8^{19}$O $\rightarrow$ _…Preview
- Q23Calculate the energy released in the following reactions, given the masses to be $_{88}^{223}$Ra: 223.0185 u, $_{82}^{209}$Pb: 208.9811 u, $…Preview
- Q24Sample of carbon obtained from any living organism has a decay rate of 15.3 decays per gram per minute. A sample of carbon obtained from ver…Preview
- Q25The half-life of $_{38}^{90}$Sr is 28 years. Determine the disintegration rate of its 5 mg sample.Preview
- Q26What is the amount of $_{27}^{60}$Co necessary to provide a radioactive source of strength 10.0 mCi, its half-life being 5.3 years?Preview
- Q27Disintegration rate of a sample is $10^{10}$ per hour at 20 hrs from the start. It reduces to $6.3\times10^9$ per hour after 30 hours. Calcu…Preview
- Q28The isotope 57Co decays by electron capture to 57Fe with a half-life of 272 d. The 57Fe nucleus is produced in an excited state, and it almo…Preview
- Q29A source contains two species of phosphorous nuclei, $_{15}^{32}$P ($T_{1/2}$ = 14.3 d) and $_{15}^{33}$P ($T_{1/2}$ = 25.3 d). At time t =…Preview
- Q30Before the year 1900 the activity per unit mass of atmospheric carbon due to the presence of 14C averaged about 0.255 Bq per gram of carbon.…Preview
- Q31How much mass of 235U is required to undergo fission each day to provide 3000 MW of thermal power? Average energy per fission is 202.79 MeV.Preview
- Q32In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundanc…Preview