Is Negative Energy Possible in the Bohr Model?

In summary, the Bohr model explains that the electron is in constant motion and has both kinetic and potential energy. The potential energy is negative due to the attractive force between the positively charged nucleus and the negatively charged electron. In order to separate a hydrogen atom completely, work must be done on it, resulting in a negative initial energy. This allows for the final energy to be zero. Alternatively, the ground state energy of hydrogen can be set to zero, but this would complicate equations. Overall, the total energy of the electron is negative due to the greater magnitude of its potential energy compared to its kinetic energy.
  • #1
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in the bohr model, the electron is in constant motion. how can such an electron have a negative amount of energy?

p.s.
sorry for clogging up this area with so many questions... I've been having a hard time understanding this area~
 
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  • #2
The potential energy (in this situation) is negative, and has a larger magnitude than the kinetic energy, which is positive. So the total energy is negative.

For mathematical convenience, we set the total energy to be zero when the electron and the proton are infinitely far apart, and at rest with respect to each other. In order to separate a hydrogen atom "completely" into this state, we have to do work on it (add energy to it). Therefore its initial energy must be negative, so that the final energy can end up as zero.

If we wanted to, we could set the ground state energy of hydrogen equal to zero. Then the "completely separated" state described above would have energy +13.6 eV. But some of our equations would become more complicated, as a result.
 
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  • #3
The electron's energy is made up of its kinetic energy and potential energy. Since the nucleus is positively charged the potential energy of the electron must decrease (charge times potential) as it gets closer to the nucleus in order for the force to be attractive. Generally, we choose the potential energy to be 0 at infinity making the potential energy negative at all finite distances. When the electron is bound to the nucleus the magnitude of the potential energy is greater than the kinetic energy.

Therefore, the total energy of the electron is negative.
 
  • #4
thank you very much! :)
 

1. What is the Bohr Model and how does it relate to negative energy?

The Bohr Model is a simplified model of the atom proposed by physicist Niels Bohr in 1913. It describes electrons orbiting the nucleus of an atom in specific energy levels. Negative energy is possible in the Bohr Model because these energy levels can have negative values, indicating that the electron has less energy than it would have at infinity.

2. How is negative energy represented in the Bohr Model?

Negative energy is represented by the negative values of the energy levels in the Bohr Model. These values indicate that the electron is in a bound state, meaning it is held in orbit by the attractive force of the nucleus. As the electron moves closer to the nucleus, its energy decreases and can become negative.

3. Is negative energy a real phenomenon in the Bohr Model or just a mathematical construct?

Negative energy is a mathematical construct in the Bohr Model, but it has real consequences. It helps explain the stability of atoms and the emission of photons when electrons move between energy levels. In reality, energy levels in atoms cannot have negative values, but the Bohr Model is a useful tool for understanding atomic behavior.

4. Can negative energy exist in other models of the atom?

Yes, negative energy can exist in other models of the atom, such as the quantum mechanical model. In this model, the energy of an electron is described by a wave function, and negative energy is represented by negative values of this function. However, the concept of negative energy is still a mathematical construct and does not have a physical manifestation.

5. Are there any potential implications of negative energy in the Bohr Model?

While the concept of negative energy is important for understanding the behavior of electrons in the Bohr Model, it does not have any significant implications in terms of practical applications. However, the understanding of negative energy in the Bohr Model has contributed to the development of quantum mechanics and our understanding of the fundamental nature of matter.

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