Chemistry Atomic Structure DUHS 2023
PMDC Verified Question 32 of 95
Radius of first orbit of hydrogen is \( 0.53\text{\AA} \). Which orbit has a radius of \( 4.77\text{\AA} \)?
A
First
B
Second
C
Third
D
Fourth
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: Third
Concept: According to Bohr's model, the radius of an electron's orbit is directly proportional to the square of its principal quantum number (\( n \)).

Formula: $$ r_n = r_1 \times n^2 $$

Solution:
  • We are given the radius of the first orbit: \( r_1 = 0.53\text{\AA} \).
  • We are given a target radius: \( r_n = 4.77\text{\AA} \).
  • Substitute the values into the formula: \( 4.77 = 0.53 \times n^2 \).
  • Divide both sides by 0.53: \( n^2 = \frac{4.77}{0.53} = 9 \).
  • Take the square root: \( n = 3 \).
  • Therefore, the orbit is the third orbit.


Why other options are incorrect: Second orbit would be \( 0.53 \times 4 = 2.12\text{\AA} \). Fourth orbit would be \( 0.53 \times 16 = 8.48\text{\AA} \).

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