Physics · Class 12 Science
Ch 12Atoms — Class 12 Physics, concept-first.
By the start of the twentieth century, physicists knew that every atom contains negatively charged electrons -- discovered by J.J. Thomson in 1897 -- embedded in some kind of positively charged material that makes the atom, taken as a whole, electrically neutral.
Key concepts
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Geiger-Marsden Alpha-Scattering Experiment
The Geiger-Marsden experiment (carried out 1908-1913, on Rutherford's suggestion) was designed to directly probe how the positive charge inside an atom is actually distributed, by firing a narrow, collimated beam of alph…
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Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
By the start of the twentieth century, physicists knew that every atom contains negatively charged electrons -- discovered by J.J.
Alpha-Particle Scattering Experiment (Geiger-Marsden Experiment)
The problem to be solved. By 1910, it was clear an atom contains electrons and an equal amount of positive charge, but the positive charge's arrangement was pure guesswork. J.J.
Impact Parameter and Distance of Closest Approach
Impact parameter. For any single alpha particle in the beam, its impact parameter is defined as the perpendicular distance between the nucleus and the line along which the alpha particle would have tr…
Rutherford's Nuclear Model of the Atom and Its Limitations
Interpreting the three observations. Rutherford drew his conclusions about atomic structure directly from the three observations of Section 1.2, reasoning as follows.
Bohr's Postulates and the Bohr Model of the Hydrogen Atom
The idea behind Bohr's model. In 1913, Niels Bohr set out to rescue Rutherford's nuclear atom (Section 1.3) from its stability and spectral problems.
Radii of the Bohr Orbits
Setting up the two conditions together. Section 1.4 gave two conditions that any allowed Bohr orbit of a hydrogen-like atom (nuclear charge , one orbiting electron) must simultaneously satisfy: the fo…
Energy Levels of the Hydrogen Atom
Total mechanical energy in an orbit. An electron in the th Bohr orbit of a hydrogen-like atom has both kinetic energy (from its orbital motion) and electrostatic potential energy (from its attraction…
The Hydrogen Spectrum: Spectral Series
From energy levels to spectral lines. Bohr's third postulate (Section 1.4) states that a photon is emitted whenever an electron jumps from a higher-energy orbit to a lower-energy orbit (), with the ph…
Elementary Theory of X-Ray Production
Turning to the innermost electrons. Sections 1.4-1.6 dealt with the OUTERMOST electron of hydrogen, whose transitions between widely-spaced outer energy levels produce visible and ultraviolet light.
Continuous and Characteristic X-Rays
Two distinct components in one beam. Spectroscopic analysis of the X-rays leaving a Coolidge tube (Section 1.7) -- plotting the intensity of X-rays produced against their wavelength -- reveals that th…
Moseley's Law
Moseley's measurements. In 1913, Henry Moseley, using an X-ray diffraction spectrometer, systematically measured the wavelength (and hence the frequency) of the characteristic X-ray line (Section 1.8)…
Summary
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
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- Q1State the postulates of Bohr's model of hydrogen atom. **OR** Define binding energy and mass defect of a nucleus. What is the relation betwe…Preview
- Q2The ratio of minimum wavelength of Lyman and Balmer series in hydrogen spectrum will be (a) 10 (b) 5 (c) 0.25 (d) 1.25Preview
- Q3a) How are the characteristic X-rays spectrum formed? b) If the value of Rydberg constant of hydrogen is 109737 cm^-1, determine the longest…Preview
- Q4What is the distance of closest approach? An α-particle having kinetic energy of 5.5 MeV is projected towards the nucleus (Z = 79). Calculat…Preview
- Q5Which of the following transitions in hydrogen atom emits a photon of lowest frequency? (a) n = 2 to n = 1 (b) n = 4 to n = 3 (c) n = 3 to n…Preview
- Q6The energy of electron in first excited state of hydrogen atom is −3.4 eV. Its potential energy in this state is (a) −3.4 eV (b) −6.8 eV (c)…Preview
- Q7What is the angular momentum of an electron in the 3rd orbit of an atom? **OR** Name the spectral series of hydrogen spectrum which lies in…Preview
- Q8In hydrogen spectrum the ratio of the minimum wavelengths of Lyman and Balmer series is (a) 1 : 4 (b) 4 : 1 (c) 5 : 4 (d) 4 : 3Preview
- Q9(a) State Bohr's postulate of quantisation of angular momentum of the orbiting electron in hydrogen atom. (b) Obtain an expression for radiu…Preview
- Q10The relation between angular momentum (L) and radius (r) of an electron revolving in a Bohr-orbit is (a) L ∝ r (b) L ∝ r⁻¹ (c) L ∝ r² (d) do…Preview
- Q11(a) The energy of the electron in the first Bohr orbit is −13.6 eV. Calculate Rydberg's constant. [1] (b) Draw the energy level diagram for…Preview
- Q12The electron of a hydrogen atom is excited to nth level. How many total possible spectral lines will be found for the transition from this e…Preview
- Q13(a) State Bohr's postulate of quantisation of angular momentum of the orbiting electron in hydrogen atom. (b) Rydberg constant in Hydrogen a…Preview
- Q14i) In which part of the electromagnetic spectrum does the spectral lines of hydrogen atom as given by Balmer series occur? ii) The energy of…Preview
- Q15i) State Moseley's law. ii) At which value of the atomic number Z of the target element, does Moseley's √v – Z plot of X-rays intersect the…Preview
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- Example 1Describe the experimental setup of the Geiger-Marsden (alpha-particle scattering) experiment on a thin gold foil, and state its three key ob…Free
- Example 2State the conclusions Rutherford drew about the structure of the atom from the results of the alpha-particle scattering experiment, and desc…Free
- Example 3State the two major limitations of Rutherford's nuclear model of the atom, explaining briefly why each was a genuine problem for classical p…Free
- Example 4State Bohr's three postulates for the hydrogen atom, explaining what each one assumes that goes beyond classical electromagnetic theory.Preview
- Example 5Using Bohr's postulates, derive an expression for the radius of the $n$th stationary orbit of an electron in a hydrogen-like atom of atomic…Preview
- Example 6Derive an expression for the total energy of an electron in the $n$th orbit of a hydrogen-like atom, and hence obtain the formula $E_n = -13…Preview
- Example 7Using Bohr's energy-level formula, derive the Rydberg formula for the wavelengths of the lines in the hydrogen spectrum, and name the spectr…Preview
- Example 8Describe, with reference to a Coolidge tube, the elementary theory of X-ray production, and distinguish between the continuous and the chara…Preview
- Example 9State Moseley's law, and explain its historical significance for the arrangement of elements in the periodic table.Preview
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- Q10Derive an expression for the distance of closest approach $r_0$ when an alpha particle is fired head-on at a nucleus of atomic number $Z$.Free
- Q11Define the impact parameter $b$ of an alpha particle in the scattering experiment, and state how it is related to the scattering angle $\the…Free
- Q12Explain, using classical electromagnetic theory, why Rutherford's model predicts that an orbiting electron should spiral into the nucleus in…Free
- Q13Explain why atomic hydrogen emits a discrete line spectrum rather than a continuous spectrum, in terms of the Bohr model's stationary orbits…Preview
- Q14Explain the physical origin of the continuous X-ray spectrum produced in an X-ray tube, and derive the expression for its short-wavelength l…Preview
- Q15Explain the physical origin of characteristic X-ray lines, describing what happens inside a target atom when an inner-shell electron is knoc…Preview
- Q16Explain, with two historical examples, how Moseley's law resolved anomalies in the periodic table that had arisen from ordering elements str…Preview
- Q17Explain why Bohr's postulate of non-radiating stationary orbits, though it contradicts classical electromagnetic theory, was necessary to ob…Preview
- Q18Explain why a beam of alpha particles, rather than a beam of electrons, was used to probe the structure of the atom in the Geiger-Marsden ex…Preview
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- Q19Calculate the radius of the first Bohr orbit of the hydrogen atom. (Take $h=6.63\times10^{-34}\ \text{J s}$, $m_e=9.1\times10^{-31}\ \text{k…Free
- Q20Calculate the radius of the second Bohr orbit of the singly ionised helium ion He$^+$ ($Z=2$), using the value of the first Bohr radius of h…Free
- Q21Calculate the energy of the electron in the $n=2$ state of the hydrogen atom, given that its ground-state energy is $-13.6$ eV.Free
- Q22Calculate the wavelength of the $H_\alpha$ line of the Balmer series of hydrogen, produced by the transition $n=3\to n=2$. (Take the Rydberg…Preview
- Q23Calculate the wavelength of the series limit of the Lyman series of hydrogen.Preview
- Q24An alpha particle of kinetic energy $5.0$ MeV is fired head-on at a gold nucleus ($Z=79$). Calculate the distance of closest approach.Preview
- Q25An X-ray tube is operated at an accelerating voltage of $40$ kV. Calculate the minimum wavelength of the continuous X-ray spectrum it produc…Preview
- Q26Using Moseley's law in the form $\nu = \dfrac{3}{4}cR(Z-1)^2$ for the $K_\alpha$ line, calculate the wavelength of the $K_\alpha$ X-ray line…Preview
- Q27Calculate the ionisation energy of the He$^+$ ion ($Z=2$) in its ground state ($n=1$).Preview