Calculate Bohr Radius of Hydrogen Atom (n=600)

In summary, the conversation is discussing a homework problem where the task is to calculate the diameter of a hydrogen atom with a given value of n. The equation used is r = n^2a_0/Z, where a_0 is a constant and r is the radius of the electron's orbit. The resulting calculation yields a diameter of 3.80e^-5m. However, the given answer states that the diameter is actually 1.90e^-5m, which is half of the calculated value. There is confusion about whether the answer should be the diameter or the radius, and it is possible that the problem statement may have mixed up the two terms or used a different atom such as helium.
  • #1
1v1Dota2RightMeow
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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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  • #2
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.
 

1. What is the formula for calculating the Bohr Radius of Hydrogen Atom?

The formula for calculating the Bohr Radius of Hydrogen Atom is:
a0 = (4πε0h2) / (μe2)
where a0 is the Bohr Radius, ε0 is the permittivity of free space, h is the Planck's constant, μ is the reduced mass of the electron-proton system, and e is the elementary charge.

2. What does n=600 represent in the calculation of the Bohr Radius?

n=600 represents the principal quantum number, which is the energy level of the electron in the Hydrogen atom. It indicates that the electron is in the 600th energy level, which is a very high energy state.

3. How is the Bohr Radius related to the size of the Hydrogen atom?

The Bohr Radius represents the distance between the nucleus and the electron in a Hydrogen atom. It is the smallest possible distance at which an electron can orbit the nucleus. Therefore, the Bohr Radius is directly related to the size of the Hydrogen atom, as it determines the size of the atom.

4. How does the Bohr Radius change with different values of n?

The Bohr Radius is inversely proportional to the principal quantum number, n. This means that as n increases, the Bohr Radius decreases, and vice versa. So, for higher energy levels (higher n values), the electron is closer to the nucleus, and the Bohr Radius is smaller.

5. Why is the Bohr Radius of Hydrogen Atom (n=600) a theoretical calculation?

The Bohr Radius of Hydrogen Atom (n=600) is a theoretical calculation because it assumes that the electron is in a perfect circular orbit around the nucleus. In reality, the electron's motion is described by quantum mechanics, and it is not possible to precisely determine its position and orbit. Therefore, the Bohr Radius is an approximation based on classical physics and is not applicable for high energy levels like n=600.

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