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## anonymous 5 years ago What is the formula to be used for this question? Please solve question no. 50. Give all the steps. The answer is D.

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1. anonymous

The radius of a nucleus with atomic number 53 is measured to be $6 * 10^{-15}$ m.

2. anonymous

In my knowledge, there isn't an explicit equation to use here. For atoms of low atomic number, the neutron to proton ratio is about 1:1. As more and more protons are added to the nucleus, however, the electrostatic repulsion between the protons becomes greater and greater. In order to compensate for this repulsion, a greater ratio of neutrons must be added to the nucleus, effectively shielding the protons from one another. It turns out, the neutron to proton ratio approaches 1.5:1 for atoms with many protons in the nucleus. This relationship can be seen graphically in what is commonly called the "Band of Stability", which is a neutron vs. proton plot for each element found in the periodic table. I've attached an image of this stability band to help you out. So to solve your problem, you would look qualitatively at the graph to see an approximate number of neutrons that should be expected from a nucleus with 53 protons; clearly, the answer is somewhere between 70 and 75, which corresponds to answer D. As for the radius information given in the problem, I think that's included to throw you off! All that is required to answer this question is the fact that you're looking at a nucleus of an atom with X number of protons. I hope that helps solidify your understanding!

3. anonymous

Thank you for replying. This was my question paper in the exam and we were not given any values (mass, etc.) or graphs. Is there any other way, may be a formula, to solve this problem? Can you in any way use this formula: R = $R _{0}$ * $\sqrt[3]{A}$ where R => radius of atom, $R _{0}$ is 1.1 * $10^{15}$ and A => atomic mass number.

4. anonymous

I don't think you'd need to do that. You know that the number of protons in the nucleus, and therefore the atomic number, is 53. You can therefore qualitatively guess a neutron to proton ratio of somewhere in the middle of 1:1 and 1.5:1 (maybe 1.25:1) without needing a graph at all. The only response that makes any sense in that regard is something in the 70's (answer D). A test taking strategy: Looking at the answer choices, they seem to vary widely in magnitude. It seems reasonable to conclude, then, that the question is testing a general concept and isn't concerned with an explicit formula or exact calculation. They want to test your understanding that the neutron to proton ratio of atoms increases as atomic number increases. The only answer choice that makes sense in that context is D. Don't just use the formulas mindlessly; think about it! Hope that helps!

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