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An α-particle of 10 MeV is moving forward for a head-on collision. What will be the distance of closest approach from the nucleus of atomic number Z=50?

Asked in GSEB Board July 2016 · Distance of closest approach

• (1) 2.88×10⁻¹⁴ m
• (2) 1.44×10⁻¹⁴ m
• (3) 0.53×10⁻¹⁰ m
• (4) (0.53×10⁻¹⁰)/(50) m

Step-by-step solution

Why the other options are wrong

• (1) 2.88×10⁻¹⁴ m takes the α-particle's charge as 4e, reading its mass number as its charge number. That doubles the Coulomb energy and so doubles r₀; the charge is 2e.
• (3) 0.53×10⁻¹⁰ m is the Bohr radius, the size of hydrogen's first electron orbit. It uses neither the 10 MeV nor Z=50, and has nothing to do with an α-particle driving into a nucleus.
• (4) Dividing the Bohr radius by Z gives the first-orbit radius of a hydrogen-like ion with Z=50 — an electron orbit again, not a closest approach set by the particle's energy.

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