Calculate Bohr Radius of Hydrogen Atom (n=600)

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SUMMARY

The discussion focuses on calculating the Bohr radius of a hydrogen atom with a principal quantum number (n) of 600 using the formula $$r=\frac{n^2a_0}{Z}$$, where $$a_0=0.529e^{-10}m$$. The calculated radius is $$r=1.90e^{-5}m$$, leading to a diameter of $$d=3.80e^{-5}m$$. The confusion arises from a discrepancy with the provided answer, which states the diameter as $$d=1.90e^{-5}m$$, indicating a possible mix-up between radius and diameter in the problem statement.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically the Bohr model.
  • Familiarity with the concept of principal quantum numbers (n).
  • Knowledge of the Bohr radius and its significance in atomic physics.
  • Basic algebra for manipulating equations and solving for variables.
NEXT STEPS
  • Study the Bohr model of the hydrogen atom in detail.
  • Learn about the implications of quantum numbers on atomic structure.
  • Explore the differences between radius and diameter in atomic physics contexts.
  • Investigate the properties of helium and its atomic structure for comparative analysis.
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Students in physics or chemistry courses, educators teaching atomic theory, and anyone interested in quantum mechanics and atomic calculations.

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I'm doing a homework problem where it asks to calculate the diameter of a hydrogen atom with n=600. I used the equation $$r=\frac{n^2a_0}{Z}$$ where $$a_0=0.529e^{-10}m$$.

Solving for r yields:

$$r=\frac{(600^2)(0.529e^{-10}m)}{1}=1.90e^{-5}m$$

Multiplying by 2 to get the diameter yields:

$$d=2r=2(1.90e^{-5}m)=3.80e^{-5}m$$

However, the answer given says that d=1.90e^-5m, but how can this be? I know that the equation above yields the radius of an electron's orbit, but why would they claim that it's the diameter? Did I miss something?
 
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I guess they mixed diameter and radius in the problem statement. Or did they use helium? I don't see other options to get a factor of 2.
 

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