PHYSICS | Class XII
Chapter 12 & 13
ATOMS AND NUCLEI
Atomic Models ◆
Bohr's Theory ◆ Nuclear Structure ◆
Radioactivity ◆ Nuclear Energy
PART A: ATOMS
The story of atomic structure is one of the most fascinating journeys in
the history of science. It spans several centuries and involved some of the
greatest minds in physics. From the primitive notion of an indivisible 'atom'
proposed by the ancient Greeks, to the sophisticated quantum mechanical model
of today, our understanding has been revolutionised by a series of landmark
experiments and bold theoretical insights.
This part covers the discovery of the nuclear atom through Rutherford's
experiment, the explanation of atomic spectra through Bohr's quantised model,
and the limitations that ultimately led to quantum mechanics.
1. Early Atomic Models
1.1 Thomson's 'Plum Pudding' Model (1904)
After the discovery of the electron in 1897, J.J. Thomson proposed the
first modern atomic model. He visualised the atom as a sphere of uniformly
distributed positive charge (like a pudding), with electrons embedded inside it
like plums in a pudding. This model explained why atoms are electrically
neutral — the total negative charge of electrons equals the total positive
charge.
Failure: Thomson's model could not explain the results of
Rutherford's scattering experiment. It predicted that alpha particles would
pass through the atom with very minor deflections — it could not account for
the large-angle scattering and back-scattering observed.
1.2 Rutherford's Nuclear Model (1911)
Ernest Rutherford, along with Hans Geiger and Ernest Marsden, performed
the famous Gold Foil Experiment (1909–1911). They directed a beam of alpha
particles (helium nuclei, charge +2e) at a very thin gold foil (about 1000
atoms thick) and observed the scattering pattern using a circular ZnS (zinc
sulphide) detector screen that flashed when hit by an alpha particle.
Figure 1: Rutherford's Gold Foil
Experiment — Most alphas pass straight through; a few deflect; very few
backscatter, revealing a dense, tiny, positive nucleus.
1.3 Observations and Conclusions
◆
Most alpha particles (> 99%) passed straight through
the gold foil without any deflection → Most of the atom is empty space.
◆
Some alpha particles were deflected through small
angles → The positive charge is concentrated in a tiny central region.
◆
A very few alpha particles (about 1 in 8000) were
deflected by very large angles, even bouncing back (180°) → There must be a
tiny, extremely dense, positively charged nucleus at the centre.
◆
The nucleus has a radius of order 10⁻¹⁵ m (femtometre
or fermi), while the atomic radius is of order 10⁻¹⁰ m (Angstrom) → The nucleus
is about 10,000 to 100,000 times smaller than the atom.
|
Distance of Closest Approach |
r₀ = k
· (2e)(Ze) / KE = k · 2Ze² / ½mv² |
|
Impact Parameter |
b =
(Ze²/4πε₀) · cot(θ/2) / KE |
Failure of Rutherford's Model: According to classical
electrodynamics, a charged particle moving in a curved path (like an electron
orbiting the nucleus) must continuously emit electromagnetic radiation and lose
energy. This would cause the electron to spiral inward and collapse into the
nucleus within about 10⁻⁸ seconds. Also, the model could not explain the
discrete spectral lines of hydrogen. A new model was urgently needed.
2. Bohr's Model of the Hydrogen Atom (1913)
Niels Bohr (1913) proposed a revolutionary new model of the atom by
combining Rutherford's nuclear model with Planck's quantum hypothesis and
Einstein's photon concept. His model, though later superseded by quantum
mechanics, brilliantly explained the hydrogen spectrum and introduced the
concept of quantisation of angular momentum.
Figure 2: Bohr's Atomic Model — Electrons
orbit in fixed, quantised shells. Photons are emitted or absorbed during
transitions between energy levels.
2.1 Bohr's Postulates
|
Bohr's Three Postulates |
|
Postulate 1 (Stable Orbits):
Electrons revolve around the nucleus in certain allowed circular orbits
called stationary states or energy levels. While in these orbits, electrons
do NOT emit radiation — they are stable. Postulate 2 (Quantisation of
Angular Momentum): The angular momentum of an electron in an allowed orbit is
an integral multiple of h/2π. That is:
L = mvr = nh/2π, where n = 1, 2, 3, ... is the principal quantum
number. Postulate 3 (Quantum Jumps):
An electron can make a transition from one stationary state to another. When
it jumps from a higher energy level E2 to a lower level E1, it emits a photon
of energy E2 − E1 = hν. When it absorbs a photon of the right energy, it
jumps to a higher level. |
2.2 Bohr's Formulae for Hydrogen-like Atoms
|
Quantisation of Angular Momentum |
mvr = n
h / 2π = n ℏ |
|
Radius of nth Orbit |
rₙ = n²
a₀ / Z = n² × 0.529 Å / Z |
|
Speed of Electron in nth Orbit |
vₙ = Z
e² / (2ε₀ h n) = 2.18 × 10⁶ × (Z/n) m/s |
|
Total Energy of nth Level |
Eₙ =
−13.6 × Z² / n² eV |
|
Frequency of Emitted Photon |
hν =
Eₙ₂ − Eₙ₁
= 13.6 Z² (1/n₁² − 1/n₂²) eV |
|
Rydberg Formula (wavenumber) |
1/λ = R∞
Z² (1/n₁² − 1/n₂²) |
Key Values: Bohr radius a₀ = 0.529 Å = 0.529 × 10⁻¹⁰ m. Rydberg constant R∞ = 1.097 × 10⁷ m⁻¹. Ground state energy of hydrogen = −13.6
eV. Ionisation energy = +13.6 eV.
For hydrogen (Z=1): E₁ = −13.6 eV, E₂ = −3.4 eV, E₃ = −1.51 eV, E₄ =
−0.85 eV, E∞ = 0 (ionised). The negative sign indicates that the electron is
bound to the nucleus — energy must be supplied to free it.
2.3 Hydrogen Spectral Series
Figure 3: Hydrogen Energy Level Diagram —
All spectral series shown. Transitions to n=1 form Lyman (UV); to n=2 form
Balmer (visible); to n=3 form Paschen (IR).
|
Spectral
Series |
Transition
to n= |
Spectral
Region |
First Line
(n₂→n₁) |
Wavelength
Range |
|
Lyman Series |
n₁ = 1 |
Ultraviolet (UV) |
n=2 → n=1 |
91.2 nm – 121.6 nm |
|
Balmer Series |
n₁ = 2 |
Visible Light |
n=3 → n=2 (656.3 nm, Red) |
364.6 nm – 656.3 nm |
|
Paschen Series |
n₁ = 3 |
Near Infrared (IR) |
n=4 → n=3 |
820.4 nm – 1875 nm |
|
Brackett Series |
n₁ = 4 |
Infrared (IR) |
n=5 → n=4 |
1458 nm – 4051 nm |
|
Pfund Series |
n₁ = 5 |
Far Infrared |
n=6 → n=5 |
2278 nm and above |
2.4 Limitations of Bohr's Model
◆
Bohr's model works only for hydrogen and hydrogen-like
ions (He⁺, Li²⁺). It fails for multi-electron atoms.
◆
It cannot explain the fine structure of spectral lines
(splitting due to spin-orbit coupling observed under high resolution).
◆
It cannot explain the relative intensities of different
spectral lines.
◆
It does not explain the Zeeman effect (splitting of
spectral lines in a magnetic field) or the Stark effect (splitting in an
electric field).
◆
It contradicts de Broglie's wave nature of electrons
and is inconsistent with Heisenberg's Uncertainty Principle.
3. de Broglie's Explanation of Bohr's Quantisation
Louis de Broglie (1924) provided a beautiful physical interpretation of
Bohr's seemingly arbitrary quantisation condition. He proposed that electrons
have wave nature with wavelength λ = h/mv. For an electron to have a stable
orbit, the de Broglie wave must form a standing wave around the orbit — meaning
the circumference of the orbit must be an integral multiple of the wavelength.
|
de Broglie Condition for Stable Orbit |
2πr =
nλ = n(h/mv) |
Rearranging: mvr = nh/2π — which is exactly Bohr's quantisation condition!
This gave Bohr's postulate a firm physical foundation: electrons exist in
orbits where their matter waves form closed, non-destructively-interfering
standing waves.
PART B: NUCLEI
The nucleus is the dense core at the centre of every atom. Despite
occupying only about 10⁻¹⁵ of the atomic volume, the nucleus contains about
99.97% of the atom's mass. The study of nuclear structure, radioactivity, and
nuclear energy is not only of profound scientific importance but also has
life-changing practical applications — from nuclear power plants and medical
imaging to cancer radiotherapy and carbon dating.
4. Nuclear Structure and Properties
4.1 Constituents of the Nucleus
Proton: Positively charged particle in the nucleus. Charge = +1.6
× 10⁻¹⁹ C. Mass = 1.00728 u = 1.673 × 10⁻²⁷ kg. Atomic number Z = number of
protons.
Neutron: Electrically neutral particle in the nucleus. Mass =
1.00866 u = 1.675 × 10⁻²⁷ kg. N = number of neutrons = A − Z.
Nucleon: Common name for protons and neutrons. Mass number A = Z +
N = total number of nucleons.
|
Nuclear Notation |
ᴬZ X where A = mass number, Z = atomic number,
X = element symbol |
|
Nuclear Radius |
R = R₀
× A^(1/3) where R₀ = 1.2 × 10⁻¹⁵ m =
1.2 fm |
|
Nuclear Density |
ρ ≈
2.3 × 10¹⁷ kg/m³ (constant for all nuclei — independent of
A) |
Nuclear density is the same for all nuclei regardless of size — this is
because both the mass and volume of a nucleus are proportional to A. The
density of nuclear matter is about 10¹⁴ times the density of water — a teaspoon
of nuclear matter would weigh about 100 million tonnes!
Figure 4: Nuclear Structure — Tightly
packed protons (red) and neutrons (blue) in the nucleus. Nuclear radius R =
R₀A^(1/3), density constant ~2.3×10¹⁷ kg/m³.
4.2 Isotopes, Isobars, and Isotones
|
Term |
Definition |
Same |
Different |
Example |
|
Isotopes |
Same element, different
mass numbers |
Z (atomic number) |
A and N |
¹H, ²H (deuterium), ³H
(tritium) |
|
Isobars |
Different elements, same
mass number |
A (mass number) |
Z and N |
¹⁴C and ¹⁴N (both A=14) |
|
Isotones |
Different elements, same
neutron number |
N (neutrons) |
Z and A |
³He and ⁴H (N=1 each; rare) |
4.3 Atomic Mass Unit (u)
The atomic mass unit (u) is defined as 1/12th of the mass of a carbon-12
(¹²C) atom.
|
1 atomic mass unit |
1 u =
1.66054 × 10⁻²⁷ kg = 931.5 MeV/c² |
This last equivalence (1 u = 931.5 MeV/c²) comes directly from Einstein's
mass-energy relation E = mc² and is extremely important in nuclear physics
calculations.
5. Mass Defect and Binding Energy
One of the most important discoveries in nuclear physics is that the mass
of a nucleus is always less than the sum of the masses of its constituent
protons and neutrons. This difference is called the Mass Defect (Δm). According
to Einstein's mass-energy equivalence (E = mc²), this missing mass has been
converted into the energy that holds the nucleus together — called the Binding
Energy.
|
Mass Defect |
Δm =
Z·mₚ + N·mₙ
− M_nucleus |
|
Binding Energy |
BE = Δm
· c² =
Δm × 931.5 MeV (if Δm in u) |
|
Binding Energy per Nucleon |
BE/A =
(Δm · c²) / A [MeV/nucleon] |
The binding energy per nucleon (BE/A) is the most useful quantity — it
measures the average stability of each nucleon in the nucleus. Plotting BE/A vs
mass number A gives the famous Binding Energy Curve:
|
Key Features of the Binding Energy Curve |
|
* BE/A rises sharply for light
nuclei (H, He, Li) then increases more slowly. * BE/A reaches a maximum of
about 8.8 MeV/nucleon near iron-56 (Fe-56) — the MOST STABLE nucleus. * Beyond Fe-56, BE/A decreases
gradually for heavier nuclei (uranium etc.). * Light nuclei (A < 20) can
release energy by FUSION (combining) — they move up the curve toward Fe. * Heavy nuclei (A > 100)
can release energy by FISSION (splitting) — they also move toward Fe on the
curve. * This curve explains why both
nuclear fission and nuclear fusion release enormous amounts of energy. |
6. Nuclear Forces
The nucleus contains protons that are positively charged and therefore
repel each other with enormous electrostatic (Coulomb) force. Yet the nucleus
is stable — the protons and neutrons are held together. This requires a much
stronger attractive force called the Strong Nuclear Force (or simply the
Nuclear Force).
|
Properties of the Nuclear Force |
|
1. Strongest force in nature:
The nuclear force is about 100 times stronger than the electromagnetic force
and 10³⁸ times stronger than gravity. 2. Short range: The nuclear
force is effective only at very short ranges — less than about 1 fm (10⁻¹⁵
m). Beyond 2–3 fm, it rapidly falls to zero. 3. Charge-independent: The
nuclear force is the same between p-p, n-n, and p-n pairs (ignoring Coulomb
repulsion between protons). 4. Saturating: Each nucleon
interacts only with its nearest neighbours — hence nuclear density is
constant. 5. Spin-dependent: The nuclear
force depends on the relative spin orientations of the interacting nucleons. 6. Non-central: Unlike gravity
or Coulomb force, it is not a simple central force. |
7. Radioactivity
Radioactivity is the spontaneous disintegration of unstable atomic nuclei
with the emission of radiation. It was discovered by Henri Becquerel in 1896,
while studying uranium salts. Marie Curie and Pierre Curie subsequently
discovered the radioactive elements polonium and radium, and Marie Curie coined
the term 'radioactivity'. Rutherford identified and named the three types of
radiation.
Radioactive decay is: Spontaneous (occurs on its own, without
external trigger), Random (we cannot predict which specific nucleus will decay
next), and Independent of physical/chemical conditions (temperature, pressure,
chemical bonding do not affect the decay rate).
Figure 5: Three Types of Radioactive
Decay — Alpha emits He-4 nucleus; Beta emits electron or positron; Gamma emits
high-energy photon. Each has different penetrating power.
7.1 Alpha (α) Decay
In alpha decay, an unstable heavy nucleus emits an alpha particle — which
is a helium-4 nucleus consisting of 2 protons and 2 neutrons (²⁴He). Alpha
particles have high ionising power but low penetrating power (stopped by a
sheet of paper or a few centimetres of air).
|
Alpha Decay |
ᴬ_Z X → ᴬ⁻⁴_(Z-2)
Y +
⁴₂He + Q |
Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He + 4.27 MeV. The Q-value represents the energy released.
For alpha decay to occur spontaneously, Q > 0 (i.e., the mass of parent >
mass of daughter + mass of alpha particle).
7.2 Beta (β) Decay
Beta decay occurs in two forms. In β⁻ decay, a neutron in the nucleus
converts to a proton with the emission of an electron (β⁻ particle) and an
anti-neutrino. In β⁺ decay, a proton converts to a neutron with emission of a
positron and a neutrino. Beta particles have moderate penetrating power
(stopped by a few mm of aluminium).
|
Beta-minus (β⁻) Decay |
ᴬ_Z X → ᴬ_(Z+1)
Y +
e⁻ + ν̄_e |
|
Beta-plus (β⁺) Decay |
ᴬ_Z X → ᴬ_(Z-1)
Y +
e⁺ + ν_e |
Neutrino: The existence of the neutrino (ν) was postulated by
Pauli in 1930 to explain the continuous energy spectrum of beta particles
(conservation of energy and momentum required a third particle). The neutrino
has near-zero mass and very weak interaction with matter — making it extremely
difficult to detect.
7.3 Gamma (γ) Decay
Gamma decay is the emission of high-energy electromagnetic photons (gamma
rays, λ ~ 10⁻¹² to 10⁻¹⁰ m) from an excited nucleus. It usually accompanies
alpha or beta decay when the daughter nucleus is left in an excited energy
state. Gamma rays do not change the mass number or atomic number — they only
carry away the excess energy. Gamma rays have the highest penetrating power
(require several centimetres of lead or concrete to be stopped).
|
Gamma Decay |
ᴬ_Z X* → ᴬ_Z
X +
γ (X* = excited nucleus) |
7.4 Comparison of α, β, γ Radiations
|
Property |
Alpha (α) |
Beta (β) |
Gamma (γ) |
|
Nature |
Helium-4 nucleus (⁴₂He) |
Electron (β⁻) or Positron
(β⁺) |
Electromagnetic photon |
|
Charge |
+2e |
−e or +e |
Zero (neutral) |
|
Mass |
4 u (≈ 6.64×10⁻²⁷ kg) |
9.11×10⁻³¹ kg |
Zero (massless) |
|
Speed |
~ 5–7% of c |
Up to 99% of c |
c (speed of light) |
|
Ionising Power |
Very High (strongest) |
Moderate |
Low (weakest) |
|
Penetrating Power |
Very Low (paper stops it) |
Moderate (Al sheet stops
it) |
Very High (Pb stops it) |
|
Deflected by E/B |
Yes (positively) |
Yes (negatively) |
No |
8. Radioactive Decay Law
The number of radioactive nuclei decaying per unit time is proportional
to the number of radioactive nuclei present at that instant. This is an
empirical law discovered by Rutherford and Soddy. Since decay is random and
spontaneous, it follows a statistical law.
|
Radioactive Decay Law |
dN/dt =
−λN → N(t)
= N₀ e^(−λt) |
|
Activity |
A =
|dN/dt| = λN
= λN₀ e^(−λt) = A₀
e^(−λt) |
|
Half-Life (T₁/₂) |
T₁/₂ =
0.693 / λ = ln2 / λ |
|
Mean Life (τ) |
τ = 1
/ λ =
T₁/₂ / ln2 = T₁/₂ / 0.693 |
|
Remaining nuclei after n half-lives |
N = N₀
/ 2ⁿ where n = t / T₁/₂ |
|
Activity Unit |
1 Becquerel
(Bq) = 1 decay/second; 1 Curie (Ci) =
3.7 × 10¹⁰ Bq |
Figure 6: Radioactive Decay Curve — N(t)
= N₀ e^(−λt). Every half-life T₁/₂, the number of nuclei (and activity) reduces
by exactly half.
At t = T₁/₂: N = N₀/2. At t =
2T₁/₂: N = N₀/4. At t = 3T₁/₂: N =
N₀/8. At t = nT₁/₂: N = N₀/2ⁿ. Note: The
decay constant λ is the probability of decay per nucleus per unit time. Mean
life τ is always greater than half-life T₁/₂ (τ = 1.44 T₁/₂).
Carbon Dating: Radioactive ¹⁴C (T₁/₂ = 5730 years) is continuously
produced in the atmosphere by cosmic ray interactions and absorbed by living
organisms. After death, ¹⁴C decays without replenishment. By measuring the
ratio of ¹⁴C to ¹²C in a sample, the age of organic material up to ~50,000
years can be determined.
9. Nuclear Energy
9.1 Nuclear Fission
Nuclear fission is the process in which a heavy nucleus (like ²³⁵U or
²³⁹Pu) absorbs a slow (thermal) neutron and splits into two lighter nuclei of
comparable mass, called fission fragments, along with the release of 2–3 fast
neutrons and a large amount of energy (~200 MeV per fission event).
|
Uranium-235 Fission (typical) |
²³⁵₉₂U +
¹₀n →
¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + ~200 MeV |
The energy released per fission (200 MeV) is about 50 million times more
than the energy released in burning one carbon atom (4 eV). This immense energy
release is due to the conversion of mass defect into energy via E = mc².
Chain Reaction: The 2–3 neutrons released in each fission event
can trigger further fissions in nearby ²³⁵U nuclei, leading to a
self-sustaining chain reaction. In a nuclear reactor, this chain reaction is
controlled by inserting neutron-absorbing control rods (boron or cadmium) and
using a moderator (heavy water or graphite) to slow down fast neutrons. In a
nuclear bomb, the chain reaction is uncontrolled and explosive.
|
Critical Mass Condition |
Multiplication
factor k = 1 (controlled), k > 1 (bomb), k < 1 (subcritical) |
9.2 Nuclear Fusion
Nuclear fusion is the process in which two light nuclei combine (fuse) to
form a heavier nucleus, releasing enormous energy. Fusion powers the Sun and
stars and is the most energy-dense process known in nature. Per kilogram of
fuel, fusion releases about 4 times more energy than fission, and millions of
times more than chemical reactions.
|
Proton-Proton Chain (in Sun) |
4 ¹₁H →
⁴₂He + 2e⁺ + 2νₑ + 2γ + 26.7 MeV |
|
Deuterium-Tritium Fusion (experimental) |
²₁H +
³₁H →
⁴₂He + ¹₀n + 17.6 MeV |
Fusion requires overcoming the enormous electrostatic repulsion between
positively charged nuclei. This requires extremely high temperatures (10⁷ to
10⁸ K) and pressures — conditions that exist naturally at the core of stars. On
Earth, achieving controlled fusion has been the goal of research for decades
(ITER project in France). The main challenges are achieving and sustaining such
extreme temperatures (plasma confinement using magnetic fields in Tokamak
reactors).
|
Fission vs Fusion — Comparison |
|
Fission: Heavy nucleus splits
into lighter ones. Fusion: Light
nuclei combine to form heavier ones. Fission: Triggered by slow
neutrons. Fusion: Requires extremely
high temperature (~10⁸ K). Fission: Releases ~200 MeV per
event. Fusion: Releases ~17.6 MeV per
D-T event (but much more per kg of fuel). Fission: Used in nuclear power
plants and atomic bombs. Fusion:
Powers stars; being researched for clean energy (ITER). Fission: Produces radioactive
waste. Fusion: Produces mainly helium
(safe) — much cleaner. Both reactions release energy
because the products have higher binding energy per nucleon than the
reactants. |
10. Master Formula Table — Atoms and Nuclei
|
Formula/Law |
Expression |
Key Points |
|
Bohr
Radius (n=1) |
a₀ = 0.529 Å |
Radius of
hydrogen ground state orbit |
|
nth Orbit
Radius |
rₙ = n²a₀/Z |
Grows as n²,
shrinks with Z |
|
Energy of
nth Level |
Eₙ = −13.6Z²/n² eV |
Ground state
(n=1) = −13.6 eV for H |
|
Photon
Frequency |
hν = E₂ − E₁ |
Emitted when
electron falls from E₂ to E₁ |
|
Rydberg
Formula |
1/λ = R∞Z²(1/n₁² − 1/n₂²) |
R∞ = 1.097 ×
10⁷ m⁻¹ |
|
Angular
Momentum |
L = nh/2π = nℏ |
Quantised; n
= 1,2,3,... |
|
Nuclear
Radius |
R = R₀A^(1/3) |
R₀ = 1.2 fm =
1.2×10⁻¹⁵ m |
|
Mass
Defect |
Δm = Zmₚ + Nmₙ − M |
M = actual
nuclear mass |
|
Binding
Energy |
BE = Δm × 931.5 MeV |
Δm in atomic
mass units (u) |
|
Decay Law |
N = N₀ e^(−λt) |
λ = decay
constant (s⁻¹) |
|
Half-Life |
T₁/₂ = 0.693/λ |
Time for N to
halve |
|
Mean Life |
τ = 1/λ = 1.44 T₁/₂ |
Average
lifetime of a nucleus |
|
Activity |
A = λN = A₀ e^(−λt) |
Unit:
Becquerel (Bq) |
|
n
Half-Lives |
N = N₀ / 2ⁿ |
n = t/T₁/₂ |
|
1 atomic
mass unit |
1 u = 931.5 MeV/c² |
From E = mc² |
|
Distance
of Approach |
r₀ = kZe²/KE × 2 |
k = 9×10⁹
Nm²C⁻² |
11. Quick Revision — Key Points
|
Atoms — Must Know |
|
* Thomson model: electrons
embedded in positive sphere. Failed to explain Rutherford's scattering. * Rutherford's experiment:
most alpha pass straight; few back-scatter → tiny, dense, positive nucleus. * Distance of closest
approach: r₀ = k·2Ze²/KE (kinetic energy of alpha particle). * Bohr's 3 postulates: (1)
stable orbits, (2) L = nh/2π, (3) photon emitted on de-excitation. * Energy of nth level: Eₙ =
−13.6Z²/n² eV. For H(Z=1): E₁=−13.6, E₂=−3.4, E₃=−1.51 eV. * Rydberg formula: 1/λ =
R∞Z²(1/n₁² − 1/n₂²). Lyman→n₁=1(UV), Balmer→n₁=2(Visible), Paschen→n₁=3(IR). * de Broglie explains Bohr:
2πr = nλ → mvr = nh/2π (standing matter waves in orbit). |
|
Nuclei — Must Know |
|
* Nucleus: Z protons + N
neutrons. R = R₀A^(1/3), R₀=1.2 fm. Nuclear density is constant ~2.3×10¹⁷
kg/m³. * 1 u = 1.66×10⁻²⁷ kg = 931.5
MeV/c². Mass defect Δm → Binding Energy BE = Δm × 931.5 MeV. * BE/A max at Fe-56 (~8.8
MeV/nucleon) → most stable. Fusion of light + Fission of heavy → both go
toward Fe. * Alpha decay: A decreases by
4, Z decreases by 2. Beta(-): Z increases by 1. Beta(+): Z decreases by 1.
Gamma: A,Z unchanged. * Decay law: N = N₀e^(−λt).
Half-life T₁/₂ = 0.693/λ. Mean life τ = 1/λ = 1.44 T₁/₂. * After n half-lives: N =
N₀/2ⁿ. Activity A = λN (unit: Becquerel; 1 Ci = 3.7×10¹⁰ Bq). * Fission: ²³⁵U + n → Ba + Kr
+ 3n + 200 MeV. Chain reaction — controlled in reactor, uncontrolled in bomb. * Fusion: 4H → He + 26.7 MeV
(in Sun). Requires T ~ 10⁸ K. Cleaner than fission, being developed (ITER). |
— End of Chapter: Atoms and Nuclei
—