# Bohr Radius - what happens when n=100?

• wombat4000
In summary, the conversation discusses the calculation of radii for permitted electron orbits in hydrogen using the Bohr Equation. It is noted that for large values of n, the system becomes relativistic and the Bohr energy levels no longer apply. The Dirac equation must be used instead. Additionally, the finite size of the proton must be considered for physical protons. The value of the radius increases with n, rather than decreasing.
wombat4000

## Homework Statement

i have been given a question that asks to me to calculate the radii of the first, second and third 'permitted' electron orbits in hydrogen. I did this fine by using the Bohr Equation, each time just changing the n value to either 2 or 3 resulting in the first value of the radius being multiplied by 4 or 9.

The next part asks me to calculate the radius when n=100, experience of answering questions makes me think that something different will happen when n is so large and that they are not looking for me to just multiply by 100000. Does anyone know what?

wombat4000 said:

## Homework Statement

i have been given a question that asks to me to calculate the radii of the first, second and third 'permitted' electron orbits in hydrogen. I did this fine by using the Bohr Equation, each time just changing the n value to either 2 or 3 resulting in the first value of the radius being multiplied by 4 or 9.

The next part asks me to calculate the radius when n=100, experience of answering questions makes me think that something different will happen when n is so large and that they are not looking for me to just multiply by 100000. Does anyone know what?

When n approaches $$1/\alpha \approx 137$$ the system becomes relativistic so the whole derivation of Bohr energy levels falls apart, one must solve the Dirac equation. But you won't notice this if you only look at the Borh radius.

For a point proton, the formula for r works for all n.
However for a physical proton of radius~1fm, the Bohr radius becomes so small for large n that the finite size of the proton must be considered.

pam said:
For a point proton, the formula for r works for all n.
However for a physical proton of radius~1fm, the Bohr radius becomes so small for large n that the finite size of the proton must be considered.

But the value increases with n, it does not decrease.

I am careless. Thank you.

## 1. What is the Bohr Radius?

The Bohr Radius is a fundamental constant in physics that represents the distance between the nucleus and the electron in a hydrogen atom at its ground state. It is denoted by the symbol a0 and has a value of approximately 0.529 Å (angstroms).

## 2. How is the Bohr Radius calculated?

The Bohr Radius is calculated using the Bohr Model of the atom, which takes into account the electrostatic forces between the positively charged nucleus and the negatively charged electron. The formula for calculating the Bohr Radius is a0 = ℏ2 / (me2ke), where ℏ is the reduced Planck's constant, me is the mass of the electron, and ke is the Coulomb constant.

## 3. What is the significance of n=100 for the Bohr Radius?

When n=100, it means that the electron in the hydrogen atom is in the 100th energy level or shell. This is a very high energy state, and the electron is located at a much greater distance from the nucleus compared to the ground state. As a result, the Bohr Radius for n=100 is significantly larger than the usual value of 0.529 Å.

## 4. How does the Bohr Radius change when n=100?

As mentioned before, the Bohr Radius increases significantly when n=100. In fact, the value of the Bohr Radius for n=100 is approximately 52.9 Å, which is 100 times larger than the ground state value. This is due to the increased energy of the electron at this high energy level, causing it to orbit at a greater distance from the nucleus.

## 5. Can the Bohr Radius for n=100 be observed in real-life?

No, the Bohr Radius for n=100 is a theoretical value that cannot be observed in real life. This is because hydrogen atoms cannot exist in such high energy states for a significant amount of time. As a result, the Bohr Radius for n=100 is only used in theoretical calculations and does not have any practical significance.

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