Question 8

The radius of the innermost electron orbit of a hydrogen atom is 5.3 ×10 ^{−11} m. What are the radii of the n = 2 and n =3 orbits?

Answer

The radius of the innermost orbit of a hydrogen atom, r_{1} = 5.3 × 10^{−11} m.

Let r_{2} be the radius of the orbit at n = 2. It is related to the radius of the innermost orbit as:

r_{2} = (n)^{2}r_{1}

= 4 x 5.3 x 10^{-11 }= 2.12 x 10^{-10} m

For n = 3, we can write the corresponding electron radius as:

r_{3} = (n)^{2} r_{1}

= 9 x 5.3 x 10^{-11} = 4.77 x 10^{-10} m

Hence, the radii of an electron for n = 2 and n = 3 orbits are 2.12 × 10^{−10} m and 4.77 × 10^{−10} m respectively.

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