Liquid drop model

liquid drop model|

1. LIQUID DROP MODEL SUBMITTED BY: SHRADDHA M. MADGHE B.SC III YR SEM 6 {MBZ} GUIDED BY: DR. A.S. BURGHATE MAM

2. CONTENTS INTRODUCTION POSTULATES OF LIQUID DROP MODEL BOHR-WHEELER THEORY OF NUCLEAR FISSION ADVANTAGE OF LIQUID DROP MODEL LIMITATIONS OF LIQUID DROP MODEL

3. INTRODUCTION The liquid drop model was first proposed by George Gamow and further developed by Niels Bohr and John Wheeler. George Gamow Niels Bohr John Wheeler

4. POSTULATES OF LIQUID DROP MODEL Nucleus is a homogeneous entity consisting of certain number of protons and neutrons. Each nucleon interacts strongly with all its neighbours . Considers the collective motion of all the nucleons. The interaction force {nuclear force} is assumed to be a short range one tending to saturation. Thus , nuclear force is similar to that of intermolecular force of attraction in a liquid drop. Nuclear force is independent of charge and spin of the nucleons. Behavior of nucleus is comparable to that of a liquid drop.

5. BOHR-WHEELER THEORY OF NUCLEAR FISSION The liquid drop model can explain the phenomenon of nuclear fission. A liquid drop has a spherical shape due to internal molecular forces responsible for surface tension. On applying a large external force, the sphere may change into on ellipsoid. If the external force is sufficiently large, ellipsoid may change into a dumb-bell shape and may even break at the narrow end into two portions. According to Bohr-wheeler theory, the nucleus behaves like a liquid drop. When the nucleus captures a neutron falling on it, it forms a compound nucleus which is highly energetic. The extra energy may set up a series of rapid oscillations in the spherical compound nucleus labelled as 'A' in Fig below. As a result of these oscillations, the shape of the nucleus may change at time form spherical to ellipsoidal, labelled as 'B' in the same Fig.

6. If the extra energy is large, oscillations may be so violent that stage 'C' and ultimately stage 'D' may be approached. The nucleus is now dumb-bell shaped and both parts of the dumb-bell which are not necessarily of equal size carry positive charge. The energy required to change the nucleus from stage 'A' to stage 'D' is called as fission barrier. The nucleus is now in critical state because once stage D' s reached, the final fission in to fragments (stage 'E') is inevitable on account of repulsion between the two fragments.

7. ADVANTAGE OF LIQUID DROP MODEL I) IT PROVIDES BASIS FOR THE EQUATION OF WEIZSACKER FOR CALCULATING THE ACCURATE BINDING ENERGIES OF NUCLEI AND HENCE THEIR ATOMIC MASSES. II) RADIOACTIVE DECAY COULD BE PREDICTED, CORRECTLY. III) IT COULD EXPLAIN NUCLEAR FISSION REACTION. IV) IT EXPLAINS THE MECHANISM OF LOW ENERGY NUCLEAR REACTIONS. V) IT PREDICTS A- AND B-EMISSION PROPERTIES. VI) CAPABLE OF EXPLAINING NUCLEAR PROPERTIES IN EXCITED STATE.

8. LIMITATIONS OF LIQUID DROP MODEL I)THE PERIODICITY IN NUCLEAR PROPERTIES AT MAGIC NUMBERS OF PROTONS AND NEUTRONS DOSE NOT FIND ANY SATISFACTORY EXPLANATION IN THIS MODEL I.E. FAILS TO EXPLAIN MAGIC NUMBERS. II) IT FAILS TO EXPLAIN THE STABILITY OF HEAVY NUCLIDES. III) THIS MODEL IS NOT CONSISTENT WITH THE P-P AND N-N PAIRING EFFECTS WHICH ARE PROMINENTLY OBSERVED IN STABLE NUCLEI. IV) THE MODEL IGNORES INDEPENDENT MOTIONS OF NUCLEONS, MAGNETIC MOMENT EFFECTS

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