Bohr Model Equations: Kinetic and Potential Energy in Hydrogen Atom

In summary, the question asks for an expression relating the kinetic energy (KE) and potential energy (PE) in the Bohr model of the hydrogen atom. The answer is KE = -PE. Additionally, the question asks for the change in potential energy (Ef - Ei) and kinetic energy (KEf - KEi) when a hydrogen atom absorbs a photon of energy E, resulting in the electron moving to a higher-energy level.
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Homework Statement



Write an expression relating the kinetic energy KE of the electron and the potential energy PE in the Bohr model of the hydrogen atom. (Use any variable or symbol stated above as necessary.)

b) Suppose a hydrogen atom absorbs a photon of energy E, resulting in the transfer of the electron to a higher-energy level. Express the resulting change in the potential energy of the system in terms of E.

(c) What is the change in the electron's kinetic energy during this process? (Use any variable or symbol stated above as necessary.)

Homework Equations



THATS THE QUESTION!

The Attempt at a Solution



KE = -PE
Ef - Ei
KEf - KEi
 
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  • #2
I don't think KE = - PE. How did you arrive at this?
I used centripetal force = electric force for a circular orbit to get the velocity and kinetic energy. I integrated F*dr in from infinity (where PE = 0) to get the PE. I found a simple relationship between KE and PE, but not that one.
 

Related to Bohr Model Equations: Kinetic and Potential Energy in Hydrogen Atom

1. What is the Bohr Model equation for Kinetic Energy in a Hydrogen Atom?

The Bohr Model equation for Kinetic Energy in a Hydrogen Atom is K = -13.6*(Z^2/n^2), where Z is the atomic number and n is the principal quantum number.

2. What is the Bohr Model equation for Potential Energy in a Hydrogen Atom?

The Bohr Model equation for Potential Energy in a Hydrogen Atom is U = -13.6*(Z^2/n), where Z is the atomic number and n is the principal quantum number.

3. How are Kinetic and Potential Energy related in a Hydrogen Atom according to the Bohr Model equations?

According to the Bohr Model equations, Kinetic Energy and Potential Energy in a Hydrogen Atom are inversely proportional. As the value of n increases, the Kinetic Energy decreases while the Potential Energy increases.

4. Can the Bohr Model equations be applied to other atoms besides Hydrogen?

Yes, the Bohr Model equations can be applied to any atom with a single electron, such as Helium, Lithium, and Beryllium. However, for atoms with multiple electrons, the equations become more complex and the Bohr Model is not an accurate representation of the atom's energy levels.

5. How does the Bohr Model explain the energy levels of a Hydrogen Atom?

The Bohr Model explains the energy levels of a Hydrogen Atom by proposing that the electron can only exist in specific orbits around the nucleus, each with a different energy level. The electron can move between these orbits by absorbing or emitting energy in the form of photons. The energy level is determined by the principal quantum number, n, and the atomic number, Z, according to the Bohr Model equations.

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