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rusak2 [61]
3 years ago
8

What quantum number of the hydrogen atom comes closest to giving a 24-nm-diameter electron orbit?

Chemistry
1 answer:
Paraphin [41]3 years ago
4 0

<em>n</em> = 15. A Bohr orbit with <em>n</em> = 15 comes closest to having a 24 nm diameter .

The formula for the radius <em>r</em> of the <em>n</em>th orbital of a hydrogen atom is

<em>r</em> = <em>n</em>^2·<em>a</em>

where

<em>a</em> = the Bohr radius = 0.0529 nm

We can solve this equation to get

<em>n</em> = √ (<em>r</em>/<em>a</em>)

If <em>d</em> = 24 nm, <em>r</em> = 12 nm.

∴ <em>n</em> = √(12 nm/0.0529 nm) = √227 = 15.1

<em>n</em> must be an integer, so <em>n</em> = 15.

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