The radius of the innermost electron orbit of a hydrogen atom is
Question:

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

Solution:

The radius of the innermost orbit of a hydrogen atom, r1 = 5.3 × 10−11 m.

Let r2 be the radius of the orbit at n = 2. It is related to the radius of the innermost orbit as:

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

$=4 \times 5.3 \times 10^{-11}=2.12 \times 10^{-10} \mathrm{~m}$

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

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

$=9 \times 5.3 \times 10^{-11}=4.77 \times 10^{-10} \mathrm{~m}$

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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