# <r> of hydrogen atom in ground state

• mmwave
In summary, the ground state of a hydrogen atom is the lowest energy state an electron can occupy and is calculated using the Rydberg formula. It is considered stable because there is no lower energy state for the electron to fall into. The probability distribution of the electron in the ground state is a spherical shape, and it is the starting point for the atomic emission spectrum. When the electron jumps to higher energy levels and falls back to the ground state, it emits a photon with a specific wavelength.

#### mmwave

Using the ground state of the hydrogen atom
Psi 1,0,0 = sqrt([pi]*a3) * e-r/a

I get <r> the expected radius as <r> = 3a/2 where a = Bohr radius.

Anybody happen to know if this correct?

It would have been cooler if the Bohr radius in physical constants were <r> and the scale factor were in Psi 1,0,0.

Yes, your calculation for the expected radius of the hydrogen atom in ground state is correct. The Bohr radius, denoted by a, is defined as the most probable distance from the nucleus to the electron in the ground state of the hydrogen atom. Therefore, your result of <r> = 3a/2 is in line with the expected radius.

As for your suggestion about using the Bohr radius in physical constants, it is a matter of convention and personal preference. Some may prefer to use the scale factor in the wavefunction, while others may prefer to use the physical constant. As long as the calculations are correct, either approach is acceptable.

Overall, your understanding and calculation for the expected radius of the hydrogen atom in ground state is correct. Keep up the good work!

## 1. What is the ground state of a hydrogen atom?

The ground state of a hydrogen atom is the lowest possible energy state that an electron can occupy. It is also known as the "n=1" state, where "n" represents the principal quantum number.

## 2. How is the energy of a hydrogen atom's ground state calculated?

The energy of a hydrogen atom's ground state can be calculated using the Rydberg formula: En = -13.6 eV/n2, where "n" is the principal quantum number. For the ground state (n=1), the energy is -13.6 eV.

## 3. Why is the ground state of a hydrogen atom considered to be stable?

The ground state of a hydrogen atom is considered to be stable because it is the lowest energy state that an electron can occupy, and therefore there is no lower energy state for the electron to fall into. This means that the electron will remain in the ground state unless energy is added to the system.

## 4. What is the probability distribution of the electron in the ground state of a hydrogen atom?

The probability distribution of the electron in the ground state of a hydrogen atom is a spherical shape, with the highest probability of finding the electron at the center of the atom. This is known as the "1s" orbital.

## 5. How does the ground state of a hydrogen atom relate to its atomic emission spectrum?

The ground state of a hydrogen atom is the starting point for the atomic emission spectrum. When energy is added to the atom, the electron can jump to higher energy levels, and when it falls back to the ground state, it emits a photon of light with a specific wavelength that corresponds to the energy difference between the two energy levels.