Question

Calculate the diameter of the fifteenth orbit of the hydrogen atom if the diameter of the innermost orbit is 1.06 A.

Answer 1

(Hint: Keep three significant figures in your answer.)

Answer 2

The radius of a Hydrogen atom's electron orbit is given by the following equation:\[r _{n}=\frac{ n ^{2}ħ^{2} }{ Zk _{e}e ^{2}m _{e} }\]where rn is the radius at a given energy level, n (n=1,2,3...); ħ is Planck's constant divided by 2π; Z is the atomic number; e is the electron charge; and me is the electron mass. Great.

You know the electron orbit radius for the ground state energy level (n=1), and you need to find the radius for the electron orbit for the 15th energy level (n=15). All you need to do is setup a ratio of r1 to r15. You should note that the only variables in the equation above that aren't constants are rn and n.

Does that help?