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Re: Totally confused on The Periodic Table

February 05, 2012 09:55AM
Hi Don,

the reason is you are not considering the total mass of the nucleus which contains a number of neutrons (as well as the binding energy of the nucleus). While Nickel may have 28 Protons in its nucleus, compared with Cobalt which has 27, Nickel has 31 Neutrons, compared with 32 neutrons in Cobalt. So while they may both have the same number of nucleons (N) in their nucleus (N=59), they have different proportions of protons and neutrons.

The big factor here is that neutrons have a slightly larger mass than the proton. In atomic units, the mass of a proton is 1.00728 u compared to the mass of a neutron of 1.008665 u. So if you do the summations you find that Cobalt will have a total nucleon mass of (27x1.00728 + 32x1.008665 = 59.47384) compared to Nickel which has (28x1.00728+31x1.008665 = 58.465175). So as you can see because of the difference in masses between the proton and neutron, Nickel has a lower mass than Cobalt, even though it is higher in atomic number on the periodic table. We can effectively neglect the mass of the electrons of the atoms, since they are about 1/1836 the mass of a proton (or 0.0005486 u), and contribute little to the overall mass of an atom.

Now, you will have noticed that the above calculation does not reproduce the measured masses. That is the above calculation gives total masses larger than the measured masses. The reason for this is that the above calculation does not factor in binding energy within the nucleus. In order for the nucleons to bind in a stable configuration, it must minimise its energy, i.e. it must get rid of some energy. You can think of it like this, in order to split the individual, you must provide more energy than their binding energy that sticks them together. Hence you put energy to the system to break it apart. So if we reverse this principle, energy must be given out in order to bind the nucleus together, and hence the energy of the nucleus is said to be minimised.

Where does this energy come from? Well it comes from the mass of the nucleons, via E=mc^2. A little bit of mass from the nucleons is given up in the form of energy to bind the nucleons into a stable configuration.

This is then the principle of nuclear energy for power and weapons. In both fusion (as in the sun, or fission in nuclear weapons or reactors, you are altering the number of nucleons within a nucleus to release energy. In fusion for example, you fuse deuterium (1 proton and one neutron) to form Helium (two protons and two neutrons). The binding energy of helium is much less than the total binding energy of the two deuterium nuclei, and so when the nuclei fuse, one gets an excess of energy (usually in the form of heat) released through the difference in binding energies of the mother and daughter products.

Fission is similar, but you are splitting a heavier nucleus into two lighter nucleus, whose total binding energies are less than the binding energy of the original nucleus. hence you get a net release of energy from the reaction.

Note, that in the above I am defining the Binding energy as negative as measured from a zero level. Thus two nucleons that are not bound will have a binding energy greater than or equal to zero, and that when bound the binding energy will be less than zero. In this convention the negative sign denotes energy subtracted from the system, and positive sign is energy added to the system. Ultimately it doesn't matter what level you define your energies with respect to as energy is a scalar quantity, just as long as you keep the maths self consistent.

Jonny




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Totally confused on The Periodic Table

Ahatmose 1109 February 05, 2012 03:39AM

» Re: Totally confused on The Periodic Table

JonnyMcA 378 February 05, 2012 09:55AM

Re: Totally confused on The Periodic Table

Ahatmose 266 February 05, 2012 02:57PM

Re: Totally confused on The Periodic Table

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Re: Totally confused on The Periodic Table

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Re: Totally confused on The Periodic Table

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Re: Totally confused on The Periodic Table

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Re: Totally confused on The Periodic Table

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Re: Totally confused on The Periodic Table

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Re: Totally confused on The Periodic Table

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Re: Totally confused on The Periodic Table

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Re: Jonny/Ahatmose

Thunderbird 350 February 08, 2012 03:02AM

Index of Refraction

Ahatmose 372 February 09, 2012 03:08AM

Re: Index of Refraction

Ahatmose 348 February 09, 2012 03:25AM

Re: Index of Refraction

JonnyMcA 1299 February 09, 2012 08:34AM

Re: Index of Refraction

Ahatmose 342 February 09, 2012 04:10PM

Index of Refraction: The solution ?

Ahatmose 371 February 09, 2012 05:41PM

Re: Index of Refraction: The solution ?

JonnyMcA 353 February 11, 2012 09:03AM

Re: Index of Refraction

JonnyMcA 344 February 11, 2012 08:59AM

Re: Index of Refraction

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Re: Index of Refraction

JonnyMcA 375 February 11, 2012 02:12PM

Re: Index of Refraction

Ahatmose 341 February 12, 2012 01:11PM

Addendum: Index of Refraction

Ahatmose 331 February 12, 2012 01:19PM

Second Addendum: Index of Refraction

Ahatmose 273 February 12, 2012 01:26PM

Third Addendum: Index of Refraction

Ahatmose 303 February 12, 2012 01:32PM

Re: Third Addendum: Index of Refraction

JonnyMcA 311 February 12, 2012 04:03PM

Re: Third Addendum: Index of Refraction

JonnyMcA 324 February 12, 2012 09:17PM

Re: Second Addendum: Index of Refraction

JonnyMcA 332 February 12, 2012 03:40PM

Re: Addendum: Index of Refraction

JonnyMcA 314 February 12, 2012 03:34PM

Re: Index of Refraction

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Re: Index of Refraction

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Re: Index of Refraction

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Re: Index of Refraction

Ahatmose 331 February 13, 2012 01:23AM

Re: Index of Refraction

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Re: Index of Refraction

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Re: Index of Refraction

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Re: Index of Refraction

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Re: Index of Refraction

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Re: Index of Refraction

Ahatmose 327 February 13, 2012 05:37PM

Re: Index of Refraction

JonnyMcA 312 February 13, 2012 07:20PM

Re: Index of Refraction

Spiros 448 April 05, 2018 02:20PM

Talk about stretching credibility: Index of Refraction

Ahatmose 336 February 13, 2012 05:48AM



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