HardChemistryHigh School (11–12)Structure of the Atom › Subatomic Particles and Atomic ModelsNumerical

Alpha particles of 6.0 MeV are fired straight at a silver nucleus, with Z = 47 and A = 108.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Alpha particles of $6.0\ \text{MeV}$ are fired straight at a silver nucleus, with $Z = 47$ and $A = 108$ . Find the distance of closest approach, and compare it with the radius of the nucleus. What energy would an alpha particle need to just reach the nucleus's surface?

Need a reminder? The key ideaShow

A small, dense, positive nucleus turns back the few alpha particles that come close. Closest approach: $d = \dfrac{2Z}{KE} \times 1.44\ \text{MeV fm}$ . Nuclear radius: $R = 1.2\ \text{fm} \times A^{1/3}$ . An atom is about $10^{5}$ times wider than its nucleus.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← The mass number of sodium is 23, and the radius of a sodium atom is about 1.86 × 10⁻¹⁰ m.Suppose Thomson's model were true, with the positive charge spread evenly through a gold atom. →

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