Modern Physics & Inventions

Every atom model in science was built to repair the failure of the one before it, and that is the easiest way to remember the order. Dalton said the atom is a tiny, solid, indivisible ball. Thomson found the electron, so the ball had to be breakable. Rutherford fired particles at gold foil and found that the positive charge sits in a tiny nucleus. Bohr then asked why the whirling electrons do not fall into that nucleus, and answered with fixed orbits. Finally Schrödinger and Heisenberg replaced neat orbits with clouds of probability. The full atomic-structure story belongs to Chemistry; here we pick up the physics of it.

Bohr's model of the hydrogen atom (1913) rests on three ideas. (1) An electron moves only in certain allowed circular orbits called stationary orbits, and while it stays in one, it does not radiate energy. (2) The allowed orbits are those in which the electron's angular momentum is a whole-number multiple of h/2π, that is L = nh/2π, where n = 1, 2, 3 … is the principal quantum number. (3) When an electron jumps from a higher orbit to a lower one it emits a photon of energy hν = E₂ − E₁; to jump up it must absorb exactly that much energy. For hydrogen the energy of the nth level is Eₙ = −13.6/n² eV, so the ground state (n = 1) is at −13.6 eV, and 13.6 eV is the energy needed to ionise a hydrogen atom. Bohr received the Nobel Prize in Physics in 1922.

Down the ladder = a photon goes OUT (emission); up the ladder = a photon must come IN (absorption). Because Eₙ = −13.6/n², the rungs get closer together as n grows, so the energy gap between successive levels keeps decreasing. Each element has its own set of levels, so its spectral lines are like a fingerprint; helium was first found in the Sun's spectrum (1868) before it was found on Earth.

Bohr's model works well for hydrogen and one-electron ions such as He⁺, but it fails for atoms with many electrons, cannot explain the finer details of spectra, and treats the electron as a tiny planet. The answer came from the quantum ideas of the 1920s. Planck (1900) said energy is given out in packets called quanta, E = hν, where h = 6.626 × 10⁻³⁴ J s is Planck's constant. De Broglie (1924) said that every moving particle has a wave, with wavelength λ = h/p; electron diffraction was later shown by Davisson and Germer (1927). Heisenberg (1927) gave the uncertainty principle: the position and momentum of a particle cannot both be known exactly at the same moment, and the more exactly one is fixed, the less exactly the other is known. Schrödinger (1926) gave the wave equation whose solutions are orbitals, regions of space where an electron is most likely to be found. This is why electrons, protons and neutrons are said to have a dual (wave and particle) nature.

Relativity is the other pillar of modern physics, and both of its parts are by Einstein. The Special Theory (1905) rests on two ideas: the laws of physics are the same for all observers moving at steady speed, and the speed of light in vacuum is the same (about 3 × 10⁸ m/s) for every such observer. From these come time dilation (a moving clock runs slow), length contraction, and the famous E = mc²: mass and energy are two forms of the same thing, so a little mass can become a great deal of energy. The General Theory (1915) treats gravity not as a pull but as the bending of space-time by mass. Its prediction that starlight bends near the Sun was confirmed during the solar eclipse of 1919.

In 1887 Heinrich Hertz noticed that a spark jumps more easily across a gap when ultraviolet light falls on it. Others soon showed that a clean metal plate, struck by light of suitable colour, throws out electrons. This is the photoelectric effect and the ejected electrons are called photoelectrons. The puzzle was that the wave theory of light, which says brighter light carries more energy, could not explain how it behaved. In 1905 Einstein solved it by saying that light arrives in tiny packets of energy called photons, each with energy E = hν. For this work he received the Nobel Prize in Physics in 1921.

What the experiments showed, and Einstein's equation. (1) For every metal there is a threshold frequency (ν₀); below it, no electrons come out, however bright the light. (2) Above it, the electrons come out instantly (in about 10⁻⁹ s), even for very dim light. (3) The number of photoelectrons (the photocurrent) is proportional to the intensity of light. (4) The maximum kinetic energy of photoelectrons depends on the frequency, not on the intensity. Einstein's reasoning: one photon gives all its energy to one electron. Part of it, the work function (φ = hν₀), is spent in pulling the electron out of the metal, and the rest becomes kinetic energy: hν = φ + KE_max. The reverse voltage that just stops the fastest photoelectrons is the stopping potential V₀, with eV₀ = KE_max.

Intensity means how MANY photons arrive; frequency means how much energy EACH photon carries. Think of a vending machine that accepts only a ₹10 coin. Radhika may carry a bag with a hundred ₹1 coins (very bright light of low frequency), yet the machine stays shut, because coins are not pooled. One ₹10 coin (one photon of high enough frequency) works at once. More ₹10 coins give more items (more electrons), but not faster ones.

Uses of photocells (photoelectric cells) include automatic doors and lifts, burglar alarms, street lights that switch on at dusk, exposure meters in cameras, reading the sound track of old films, counting machines and smoke detectors. Metals with a low work function, such as caesium, potassium and sodium, are used because they respond even to visible light. Do not confuse this with a solar cell: it works by the photovoltaic effect at a semiconductor p-n junction, producing a voltage, and not by throwing electrons out of a metal.

Dual nature. Light shows its wave side in interference, diffraction and polarisation, and its particle side in the photoelectric effect and in the Compton effect (1923), where X-ray photons collide with electrons like billiard balls (Nobel Prize 1927). A photon has energy E = hν = hc/λ, momentum p = h/λ, travels at the speed of light and has zero rest mass. In 1924 de Broglie turned the idea around: if waves can act like particles, particles can act like waves, with λ = h/mv. For a cricket ball this wavelength is unimaginably small, so we never notice it; for an electron it is comparable to atomic sizes, which is why electrons show diffraction and why the electron microscope (which uses electron waves of very short wavelength) can see far finer detail than an optical microscope.

In 1896 Henri Becquerel left some uranium salt on a wrapped photographic plate in a drawer and found the plate fogged, though no light had touched it. The salt was giving out invisible rays by itself. Marie and Pierre Curie then isolated two new radioactive elements from pitchblende in 1898: polonium (named after Marie's homeland, Poland) and radium. Becquerel and the Curies shared the Nobel Prize in Physics in 1903, and Marie Curie won a second one, in Chemistry in 1911. Radioactivity is the spontaneous breaking up of unstable nuclei with the emission of radiation. It is a nuclear property: heating, cooling, pressure or chemical combination do not change it. In general, nuclei with too many neutrons or protons are unstable, and all elements beyond bismuth (atomic number above 83) are radioactive. In 1934 Irène Curie and Frédéric Joliot made the first artificial radioactive isotopes.

What happens to the nucleus (Soddy-Fajans displacement laws). In alpha decay the nucleus throws out a helium nucleus, so the mass number falls by 4 and the atomic number by 2 (²³⁸U → ²³⁴Th + ⁴He). In beta-minus (β⁻) decay a neutron changes into a proton, an electron and an antineutrino (n → p + e⁻ + ν̄); the atomic number rises by 1 and the mass number stays the same (²³⁴Th → ²³⁴Pa). In beta-plus (β⁺) decay a proton changes into a neutron, a positron and a neutrino (p → n + e⁺ + ν); the atomic number falls by 1 and the mass number stays the same. In gamma emission the nucleus only drops from an excited state to a lower one, so neither Z nor A changes. Note that the beta electron comes from the nucleus, not from the electron shells. The uranium-238 series finally ends in stable lead-206.

Half-life (T½) is the time in which half of the radioactive nuclei in a sample decay. It is a fixed property of each isotope, and after n half-lives the amount left is the original divided by 2ⁿ, that is N = N₀ (½)^(t/T½). Example: a 100 mg sample with half-life 20 days leaves 50 mg after 20 days, 25 mg after 40 days and 12.5 mg after 60 days. A sample is 75% decayed (25% left) after two half-lives, and 87.5% decayed after three. A short half-life means the substance decays quickly and is intensely active; a long half-life means it decays slowly. Radiocarbon dating uses carbon-14 (half-life about 5,730 years): living things keep taking in C-14, but after death the stock only decays, so the C-14 that remains tells the age of wood, bones or cloth up to about 50,000 years (Willard Libby, Nobel Prize in Chemistry 1960). For very old rocks, the uranium-lead method is used.

Measuring radioactivity. The SI unit of activity is the becquerel (Bq) = one disintegration per second. The older unit, the curie (Ci), is named after the Curies and equals 3.7 × 10¹⁰ Bq (roughly the activity of 1 g of radium); the rutherford is 10⁶ disintegrations per second. The energy absorbed by a body is measured in gray (Gy) (1 joule per kilogram), and the biological effect in sievert (Sv); the older exposure unit is the roentgen. Radiation is detected by the Geiger-Müller counter (a gas tube that clicks for each particle), the Wilson cloud chamber and film badges. Uses: cobalt-60 for cancer treatment, sterilising medical tools and preserving food; iodine-131 for thyroid; phosphorus-32 and sodium-24 as tracers; americium-241 (alpha source) in household smoke detectors. Hazards: radiation burns, cancer and genetic damage, so workers use lead shields and dosimeters. Accidents such as Chernobyl (1986) and Fukushima (2011) show why.

Weigh a nucleus and you will find it is slightly lighter than the sum of its separate protons and neutrons. The missing mass (the mass defect) has gone out as energy that holds the nucleus together, the binding energy, by Einstein's E = mc² (1 u of mass is equivalent to about 931 MeV). The binding energy per nucleon is highest near iron-56, the most stable region. So there are two ways to release energy: split a very heavy nucleus such as uranium into middle-sized pieces (fission), or join very light nuclei such as hydrogen into a heavier one (fusion). In both, the products are more tightly bound than the starting nuclei and the small loss of mass appears as a large amount of energy.

Fission. In December 1938 Otto Hahn and Fritz Strassmann found barium in uranium that had been hit by neutrons; Lise Meitner and Otto Frisch explained that the uranium nucleus had split, and named the process fission. When a slow neutron strikes uranium-235, the nucleus splits into two medium nuclei (for example barium and krypton), releases about 200 MeV and gives out 2 or 3 fresh neutrons. If these neutrons split more nuclei, a chain reaction follows. A chain reaction that goes unchecked is an atom bomb (Hiroshima: uranium, 6 August 1945; Nagasaki: plutonium, 9 August 1945). If it is kept steady by absorbing the extra neutrons, it is a nuclear reactor. The first controlled chain reaction was achieved by Enrico Fermi at Chicago in 1942. The least amount of fissile material that can sustain a chain reaction is the critical mass. Fissile fuels are uranium-235, plutonium-239 and uranium-233.

A nuclear reactor has five main parts. The fuel is natural or enriched uranium (or plutonium). The moderator (heavy water, graphite or ordinary water) slows the fast neutrons so that they can split uranium-235. Control rods of boron or cadmium absorb neutrons and regulate the reaction. The coolant (water, heavy water or liquid sodium) carries the heat away to make steam for a turbine. Thick concrete and lead shielding guards against radiation. A breeder reactor makes more fissile fuel than it burns: uranium-238 turns into plutonium-239, and thorium-232 turns into uranium-233. India's power reactors are mostly pressurised heavy water reactors (PHWR), which run on natural uranium with heavy water as the moderator.

Fusion is the joining of light nuclei, for example deuterium and tritium (isotopes of hydrogen) forming helium and a neutron, with about 17.6 MeV released: ²H + ³H → ⁴He + n. The positively charged nuclei repel each other strongly, so fusion needs temperatures of millions of kelvin and very high pressure (it is therefore called thermonuclear reaction). This is how the Sun and the stars shine; in the Sun, four hydrogen nuclei finally become one helium nucleus. The hydrogen bomb is a fusion weapon, set off by a fission bomb that supplies the heat. Controlled fusion for power is still experimental (the international ITER project in France). Fusion fuel is plentiful (deuterium from seawater) and the waste is much less long-lived than from fission.

India's nuclear programme. Homi Jehangir Bhabha is the father of India's nuclear programme. He founded the Tata Institute of Fundamental Research (TIFR) in Mumbai in 1945 and became its first director; the Atomic Energy Commission followed in 1948 and the Department of Atomic Energy (DAE) in 1954. Research is carried out at the Bhabha Atomic Research Centre (BARC), Trombay, Mumbai (set up in 1954 and named after Bhabha in 1967), and at the Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, Tamil Nadu. Power plants are run by the Nuclear Power Corporation of India Ltd (NPCIL). Bhabha's three-stage plan is designed around India's small uranium but very large thorium reserves (monazite sands of Kerala, Odisha and Tamil Nadu): Stage 1 PHWRs burn natural uranium and make plutonium; Stage 2 fast breeder reactors use that plutonium and breed uranium-233 from thorium; Stage 3 reactors run on thorium-uranium-233.

LASER stands for Light Amplification by Stimulated Emission of Radiation. In ordinary light (a bulb) atoms emit photons at random times, in all directions and in many colours. In a laser, one photon passing an excited atom makes it release a second photon that is an exact copy: same colour, same direction, same phase. This is stimulated emission, an idea Einstein put forward in 1917. If more atoms are in the excited state than in the ground state (population inversion) and the light bounces between two mirrors, the copies multiply into a powerful narrow beam. The first working laser was the ruby laser built by Theodore Maiman in 1960. Earlier, Charles Townes made the microwave version, the maser (1954); Townes, Basov and Prokhorov shared the Nobel Prize in Physics in 1964.

More uses of lasers: eye surgery (LASIK corrects eyesight, and lasers repair a detached retina); cutting and welding in factories; distance measurement (LIDAR, and laser range-finding of the Moon using reflector arrays left by Apollo missions, and the laser retroreflector carried on Chandrayaan-3); barcode scanners and laser printers; holography (Dennis Gabor, 1947, Nobel Prize 1971); sending data through optical fibres; and detecting gravitational waves (LIGO). The danger is to the eye: even a small laser pointer should never be shone at a person's eyes.

X-rays. On 8 November 1895 Wilhelm Conrad Röntgen (Germany) saw a screen glow near a covered discharge tube and realised that some unknown ray was passing through the cardboard. He called it X-ray ('X' for unknown). In 1901 he received the first Nobel Prize in Physics. X-rays are electromagnetic waves of very short wavelength (roughly 0.01 to 10 nanometres), carrying more energy than ultraviolet. They are produced when fast-moving electrons strike a heavy metal target (tungsten or molybdenum) in a Coolidge tube; the sudden stopping of the electrons turns their kinetic energy into X-rays. They are not deflected by electric or magnetic fields, they affect photographic film, they ionise gases and they make some substances fluoresce. They pass easily through flesh but are stopped by bones and metals, which is why a bone shows up white on an X-ray film.

Semiconductor electronics. The transistor was invented in 1947 at Bell Laboratories by John Bardeen, Walter Brattain and William Shockley (Nobel Prize 1956). It replaced bulky vacuum tubes and made modern electronics possible. The integrated circuit (IC), many transistors on one silicon chip, followed in 1958-59 (Jack Kilby and Robert Noyce); the first microprocessor (Intel 4004) came in 1971; Moore's law says the number of transistors on a chip doubles about every two years. The working of p-n junctions is explained in the Electricity chapter; the table below lists what each device is used for.

Logic gates are the building blocks of digital circuits. AND gives 1 only when all inputs are 1; OR gives 1 when any input is 1; NOT reverses the input; NAND (NOT-AND) and NOR (NOT-OR) are called universal gates because any other gate can be built from either of them alone.

Questions on inventors are pure 'who and when' questions, so the way to win them is to attach each invention to a short story and a year. Remember two things first. An invention is making something new that did not exist (the telephone), while a discovery is finding something that was already there (radioactivity, the electron). And many inventions were improved by a second person, so exams usually ask for the person who is most credited: Newcomen built an early steam engine but Watt made it efficient; Hans Lippershey applied for the first telescope patent but Galileo used it for the sky. The tables below group the well-known inventions by field.

Instruments and machines.

Electricity, communication and media.

Everyday objects, medicine and modern science.

Science honours its heroes by putting their names on units. The way of writing is simple: the name of the unit is written in small letters (newton, joule, kelvin), but its symbol starts with a capital letter (N, J, K). Of the seven SI base units, only two are named after people: the ampere (André-Marie Ampère) and the kelvin (Lord Kelvin). The metre, kilogram, second, mole and candela are not. Most of the others are derived units. Learn them as three groups: mechanics and heat, electricity and magnetism, and radiation.

Indian physicists and the Nobel Prize. Sir C. V. Raman (Chandrasekhara Venkata Raman) discovered on 28 February 1928 that when light is scattered by molecules, a small part of it changes its wavelength; this is the Raman effect. He received the Nobel Prize in Physics in 1930, the first Asian to win a Nobel Prize in science, and India observes National Science Day on 28 February in memory of the discovery. Raman worked in Kolkata (at the Indian Association for the Cultivation of Science) and later in Bengaluru, where he founded the Raman Research Institute (1948). His nephew Subrahmanyan Chandrasekhar received the Nobel Prize in Physics in 1983 (shared with W. A. Fowler) for his studies of the structure and evolution of stars; the Chandrasekhar limit (about 1.4 times the Sun's mass) is the largest mass a white dwarf star can have. Chandrasekhar lived and worked in the USA.

Remember also the other Indian-born Nobel laureates in the sciences: Har Gobind Khorana (Medicine, 1968, for the genetic code) and Venkatraman Ramakrishnan (Chemistry, 2009, for the structure of the ribosome). Both, like Chandrasekhar, held citizenship of another country when they won; Raman is the one who received the prize as an Indian working in India. Marie Curie and Röntgen, the names behind the units in this topic, are linked to radioactivity and X-rays; Marie Curie remains the first person to win Nobel Prizes in two different sciences (Physics 1903, Chemistry 1911).