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Bohr orbits: orbital radius and orbital speed

Problem

According to Bohr's model of the hydrogen atom, the radius of the fourth orbital, r, start subscript, 4, end subscript, equals, 8, point, 464, space, start text, A, with, \r, on top, end text.
(Imagine how tiny that is compared to the shortest wavelength of visible light, which is around 3800, space, start text, A, with, \r, on top, end text.)
What is the radius of the fifth orbital, r, start subscript, 5, end subscript?
Note: Let's use only the given value of r, start subscript, 4, end subscript, and input the answer upto three decimal places.
r, start subscript, 5, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
start text, A, with, \r, on top, end text
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Stuck?