In the fifth energy level determine the radius and energy of electron for the hydrogen atom? (Answer: 1.323 nm, -8.72 x 10⁻²⁰ J or -0.545 eV) 



Data Given:

Hydrogen Atom 

Energy Level n = 5


To Find:

(a) Radius of the 5th energy level = `\r_5` =  ?

(b) Energy of the 5th energy level = `\E_5` =  ?



Solution:

(a) Radius of the 5th energy level = `\r_5` =  ?

The general formula for the radius of quantized orbit for a Hydrogen atom is 

`\r_n` = 0.053 nm ｘn²

for n = 5

`\r_5` = 0.053 nm ｘ(5)²

`\r_5` = 0.053 nm ｘ25

`\r_5` = 1.325 nm  ------------------Ans.1




(b) Energy of the 5th energy level = `\E_5` =  ?

The general formula for the radius of quantized orbit for a Hydrogen atom is 

`\E_n` = -`\frac {E_0}{n^2}`

Where `\E_0` = constant = 2.179 ｘ10⁻¹⁸ J  = 13.6 eV and n = 5 So,


`\E_n` = - `\frac {2.179 ｘ10⁻¹⁸ J}{5^2}`

`\E_n` = - `\frac {2.179 ｘ10⁻¹⁸ J}{25}`

`\E_n` = - 0.08716 ｘ10⁻¹⁸ J

`\E_n` = - 8.72 ｘ10⁻²⁰ J  ----------------Ans.2


in eV  ( 1 eV = 1.602 ｘ10⁻¹⁹ J)

`\E_n` = - `\frac {8.72 ｘ10⁻²⁰ }{1.6 ｘ10⁻¹⁹}` eV

`\E_n` = - 5.45 ｘ10⁻¹ eV

or

`\E_n` = - 0.545  eV  ----------------Ans. 3




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