By Laura Gonzalez,2014-06-02 04:06
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(c) In Fig. c, the particle approaches the nucleus head-on and is therefore deflected backwards, i.e. through an angle of 1800. The electrostatic force F between particle with positive nucleus is inversely proportional ......

    AL Physics/Matter/The Nucleus K.W. LAM

    The Nucleus

1. The Rutherford Model of the Atom

1.1 Rutherford Scattering Experiment

     To shoot particles (of several MeV energy) at a piece of very thin gold foil (about ;510 m thick).

     An particle penetrates the gold foil and may hit an atom.

     It is then scattered (i.e. changes direction) and comes out of the gold foil with some

    deflection angle.

     A microscope M is turned through different angles. The number of scattering events

    observed at different angles of deflection are recorded.

     The following results are obtained:

    (a) Most of the particles come out with very

    small deflections (Fig. a).

    (b) Some of the particles come out with large

    deflections (Fig. b).

    (c) Few particles come out with deflections close 0to 180 (Fig. c).

    Q: How do we know there is a scattered particle reaching the microscope?

    A: There is a fluorescent screen (similar to that in a CRO) at the focal length of the

    microscope. Whenever it is hit by a high-speed charged particle, it glows and the glow

    of light (called scintillation) is detected in the microscope.

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    AL Physics/Matter/The Nucleus K.W. LAM

    1.2 Rutherford’s Model of the Atom

     Based on the experimental results,

    Rutherford assumed that

     Most of the mass and all of its positive charge are concentrated in a tiny region at

    the centre of the atom, called the atomic nucleus, or simply nucleus.

     Under the attractive influence of the positively charged nucleus, a number of

    negatively charged electrons move around the nucleus like a cloud. These are

    called ‘extra-nuclear’ electrons.

    Rutherford's model (not to scale)

This model can explain the result of scattering experiment.

     Consider the situations in the diagram.

    (a) In Fig. a, the particle passes the

    nucleus at a fairly large distance b from

    the centre of the nucleus. It is not

    subjected to a strong repulsive force

    and is therefore deflected only slightly.

    (b) In Fig. b, the distance b is smaller, the

     particle gets closer to the nucleus and

    experience a stronger repulsive force,

    so there is a larger deflection.

    (c) In Fig. c, the particle approaches the

    nucleus head-on and is therefore

    deflected backwards, i.e. through an 0angle of 180.

    The electrostatic force F between particle with positive nucleus is inversely

    proportional to the square of the separation b, i.e.

    1F 2b

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    AL Physics/Matter/The Nucleus K.W. LAM

     ;10 Atomic radius of a nucleus is of order 10 m

     ;15 While the radius of a nucleus is of order 10 m ;15;15(in the range from 1 × 10 m to 8 × 10 m, ;15;15e.g. hydrogen nucleus 1 10 m; uranium nucleus 7 ×10 m).

     It should be noted that most of the volume of an atom is empty space.

     So if we scale up the whole atom to the size of Hong Kong, then the nucleus would be

    about the size of a man! The electron would be even smaller (e.g. a file).


    Rutherford's model could not explain the existence of the characteristic atomic line

    spectra from atoms of a particular element.

1.3 Inside the Nucleus

     The nucleus has protons and neutrons

    (A) Protons

     A proton carries one unit of positive charge +e. In other words, its charge is

    ;19 qp = +e = +1.6 × 10 C

     In S.I. units, the proton mass is

    ;27 mp = 1.67 × 10 kg

     The proton number (or atomic number) Z shows the chemical nature of the


    (B) Neutrons

     A neutron has roughly the same mass as the proton, but it carries NO charge.

     In S.I. units, the neutron mass is

    ;27 mn = 1.675 × 10 kg

     Number of neutrons is denoted by N.

    (C) Extra-nuclear Electrons (Outside the nucleus)

     An electron carries one unit of negative charge -e.

    ;19 qe = ;e = ;1.6 × 10 C

     The electron mass is very small and is about 1/1840 of the mass of a proton.

     In a neutral atom, the number of electrons equals the number of protons.

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AL Physics/Matter/The Nucleus K.W. LAM

    (D) Packing of Nucleons

     A proton or a neutron is collectively called a nucleon.

     The number of nucleon A = number of proton Z + number of neutron N, i.e. A =

    Z + N.

     The number of nucleons A is approximately the same as the mass (in unit of

    proton mass or neutron mass) of the whole atom.

    4Hee.g. Number of nucleon of a nucleus is 4, 2

     so mass of the nucleus = 4 units of proton mass (or neutron mass).

     As we have learnt that an atom is very empty, so the nucleus and the electrons

    occupy a very small portion of volume.

     In contrast, the nucleons inside a nucleus are with packed very tightly

    almost no empty space.

1.4 Gravitational Analogy

    Related AL Questions: [85/IIA/5]

2. The Mass-Energy Relationship

2.1 Einstein’s Mass-Energy Relation

     In 1905, Einstein showed from his theory of relativity that mass (m) and energy (E)

    can be changed from one form to another.

    2E = mc

     where E ; energy is measured in J

     m ; mass is measured in kg 8;1 c ; speed of light = 3 × 10 ms

     Then mass of 1 kg can be changed to (or is equivalent to) energy 8216= (1)(3 × 10) = 9 × 10 J


    (a) Find the energy in J equivalent to the mass of 1 g.

    (b) Convert the energy in J to kWh; hence deduce how long is the amount of energy

    sufficient to keep an electrical lamp burning in a house.

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    AL Physics/Matter/The Nucleus K.W. LAM


     2(a) E = mc


     So a mass of 1 g is sufficient to keep the electrical lamps in ____________ houses

    burning for about ___________, on the basis of about 7 hours’ use per day.

2.2 The Unified Atomic Mass Unit

    The unified atomic mass unit (denoted as a.m.u. or simply u) is defined as 1/12 of the

    12mass of the carbon atom C6

    112 i.e. 1 u = (mass of a atom) C612

    12 Then mass of one atom = ________ u. C6

    Q: What is the mass of 1 a.m.u. in kg?

    112A: 1 u = (mass of a atom) C612