The document describes the liquid drop model of the atomic nucleus. It proposes that nuclear forces can be modeled as analogous to the intermolecular forces in a liquid drop. Key similarities include the nucleus being spherical, density being independent of volume, short-range forces between nucleons like molecules, evaporation of particles with increased energy, and fission producing smaller nuclei like oscillating drops splitting. The model can derive an expression for nuclear binding energy.

1. • In the liquid-drop model, the forces acting in the nucleus are
assumed to be analogical to the molecular forces in a droplet
of some liquid.
• This model was proposed by Neils Bohr who observed that
there are certain marked similarities between an atomic
nucleus and a liquid drop.

2. • The nucleus is supposed to be spherical in shape
in the stable state, just as a liquid drop is
spherical due to the symmetrical surface tension
forces.
• The force of surface tension acts on the surface of
the liquid drop. Similarly, there is a potential
barrier at the surface of the nucleus.
• The density of a liquid-drop is independent of its
volume. Similarly, the density of the nucleus is
independent of its volume.

3. • The intermolecular forces in a liquid are short
range forces. The molecules in a liquid drop
interact only with their immediate neighbours.
• Similarly, the nuclear forces are short range
forces. Nucleons in the nucleus also interact
only with their immediate neighbours. This
leads to the saturation in the nuclear forces
and a constant binding energy per nucleon

4. • The molecules evaporate from a liquid drop
on raising the temperature of the liquid due to
their increased energy of thermal agitation.
• Similarly, when energy is given to a nucleus by
bombarding it with nuclear projectiles, a
compound nucleus is formed which emits
nuclear radiations almost immediately.

5. • When a small drop of liquid is allowed to
oscillate, it breaks up into two smaller drops
of equal size.
• The process of nuclear fission is similar and
the nucleus breaks up into two smaller nuclei.

6. • The liquid-drop model can be used to obtain
an expression for the binding energy of the
nucleus.
• Weizacker proposed the semi-empirical
nuclear binding energy formula for a nucleus
of mass number A, containing Z protons and N
neutrons.

7. • The first term is called the volume energy of a
nucleus (Ev = aA).
• The larger the total number of nucleons A, the
more difficult it will be to remove the
individual protons and neutrons from the
nucleus.
• The B. E. is directly proportional to the total
number of nucleons A.

8. • The nucleons, at the surface of the nucleus,
are not completely surrounded by other
nucleons.
• Hence energy of the nucleon on the surface is
less than that in the interior. The number of
surface nucleons depends upon the surface
area of the nucleus

9. • The electrostatic repulsion between each pair
of protons in a nucleus also contributes
towards decreasing its B.E.
• The Coulomb energy Ec of a nucleus is the
work that must be done to bring together Z
protons from infinity into a volume equal to
that of the nucleus.

10. • A Geiger counter (Geiger-Muller tube) is a
device used for the detection and
measurement of all types of radiation: alpha,
beta and gamma radiation.
• Basically it consists of a pair of electrodes
surrounded by a gas.
• The electrodes have a high voltage across them.
The gas used is usually Helium or Argon.
• When radiation enters the tube it can ionize the
gas.
• The ions (and electrons) are attracted to the
electrodes and an electric current is produced.
• A scalar counts the current pulses, and one
obtains a ”count” whenever radiation ionizes
the gas.

11. • The apparatus consists of two parts, the tube and the (counter +
power supply).
• When ionizing radiation such as an alpha, beta or gamma particle
enters the tube, it can ionize some of the gas molecules in the tube.
• From these ionized atoms, an electron is knocked out of the atom,
and the remaining atom is positively charged.
• The high voltage in the tube produces an electric field inside the
tube.
• The electrons that were knocked out of the atom are attracted to
the positive electrode, and the positively charged ions are attracted
to the negative electrode.
• This produces a pulse of current in the wires connecting the
electrodes, and this pulse is counted.
• After the pulse is counted, the charged ions become neutralized,
and the Geiger counter is ready to record another pulse.

12. • The efficiency of a detector is given by the
ratio of the (number of particles of radiation
detected)/(number of particles of radiation
emitted)
• ε ≡ number of particles of radiation detected
_____________________________________
number of particles of radiation emitted

13. • They are relatively inexpensive.
• They are durable and easily portable.
• They can detect all types of radiation

14. • They cannot differentiate which type of
radiation is being detected.
• They cannot be used to determine the exact
energy of the detected radiation.
• They have a very low efficiency

15. • A Cloud Chamber is a device used to detect
ionizing particles and to determine their
trajectories.

16. 1. Liquid is placed into a
chamber and allowed to
reach an equilibrium state of
evaporation and
condensation. (saturation)
2. Chamber is adiabatically
cooled or expanded, resulting
in supersaturation of the air
inside. (disruptions will cause
quick & easy condensation)

17. 3. Ionizing radiation passing
through the vapor ionize
nearby atoms and
molecules.
4. Condensation occurs around
ionized molecules, revealing
the path of the ionizing
particles.

18. The Cyclotron
• A cyclotron is a machine that accelerates
charged particles or ions to high energies. It
was invented to investigate the nuclear
structure by E.O Lawrence and M.S Livingston
in 1934.

20. • A cyclotron accelerates a charged particle beam
using a high frequency alternating voltage which
is applied between two hollow “D”-shaped sheet
metal electrodes known as the “dees” inside a
vacuum chamber.
• The dees are placed face to face with a narrow
gap between them, creating a cylindrical space
within them for particles to move. Particles are
injected into the center of this space.

21. • Dees are located between the poles of
electromagnet which applies a static magnetic
field B perpendicular to the electrode plane.
• The magnetic field causes the path of the
particle to bend in a circle due to the Lorentz
force perpendicular to their direction of
motion.

22. • An alternating voltage of several thousand volts
are applied between the dees. The voltage
creates an oscillating electric field in the gap
between the dees that accelerates the particles.
• The frequency of the voltage is set so that
particles make one circuit during a single cycle of
the voltage. To achieve this condition, the
frequency must be set to particle’s cyclotron
frequency.