One of the fundamental laws in physics is conservation of energy. Therefore, when an electron moves between two stationary Bohr orbits, its energy needs to change. When this transition takes place, energy is either released or absorbed by the atom in form of a photon. The energy released can be calculated using the energy difference between the two stationary orbits. However, it is common to see that potential energy is neglected in such problems as we only include kinetic energy in the equation. Here, we will try to understand why potential energy is ignored in this problem for calculating the energy difference between the two stationary Bohr orbits.
Understanding Bohr’s Model of Atom
Before we get into the topic of why potential energy is ignored in calculating energy difference between two stationary Bohr orbits, let’s first understand the Bohr model of the atom. The Bohr model is one of the earliest atomic models proposed by physicist Niels Bohr. In this model, an electron moves around the positively charged nucleus in circular orbits. Bohr also postulated that electrons could only occupy fixed energy states or stationary orbits.
The fixed energy states or stationary orbits in the Bohr model are determined by the following equation:
Where,
m is the mass of the electron
v is the velocity of the electron
r is the radius of the circular orbit
n is the principal quantum number (1, 2, 3, …, ∞)
ℏ is the Planck constant divided by 2π
In the Bohr model, an electron can move to another stationary orbit by either absorbing or releasing energy. When energy is absorbed, the electron moves to a higher energy state or stationary orbit. Conversely, when energy is released, the electron moves to a lower energy state or stationary orbit. In either case, the energy absorbed/released can be calculated using the energy difference between the two stationary orbits.
Ignoring Potential Energy in Energy Difference Calculations
Now, let’s return to our original question of why potential energy is neglected when calculating energy difference between two stationary Bohr orbits. The reason for this is that potential energy is a function of the distance between two particles and only the kinetic energy contributes to the energy of the electron that is confined to a fixed orbit in the Bohr model. The potential energy contribution is constant as long as the electron is constrained on the circular orbit. The electron cannot move beyond or approach closer to the nucleus because it can only occupy fixed energy states. Therefore, the potential energy remains constant for both initial and final stationary orbits.
As a result, in problems involving stationary Bohr orbits, we only need to take kinetic energy into account. Kinetic energy is the energy possessed by the electron due to its motion. The kinetic energy of an electron in the Bohr model can be calculated using the following equation:
Where,
m is the mass of the electron
v is the velocity of the electron
When an electron moves from an initial stationary orbit to a final orbit, its kinetic energy changes, and this change in kinetic energy is equal to the energy difference between the two stationary orbits. This energy difference can be calculated using the following equation:
Where,
m is the mass of the electron
vf is the final velocity of the electron
vi is the initial velocity of the electron
Once we have calculated the energy difference between the two stationary orbits using the above equation, we can use the equation to calculate the wavelength of the photon emitted due to the transition of the electron between the two stationary orbits.
Conclusion
In summary, potential energy is ignored in calculating energy difference between two stationary Bohr orbits because it is constant for both initial and final stationary orbits, and therefore does not contribute to the calculation. Only the kinetic energy of the electron changes in a transition between two stationary orbits, and this change in kinetic energy is equal to the energy difference between the initial and final stationary orbits. This energy difference can be used to calculate the wavelength of the photon emitted when an electron undergoes a transition between two stationary Bohr orbits.
Why Potential Energy is Neglected In This Problem For Calculating the Energy Difference Between Two Stationary Bohr Orbits?
One of the fundamental laws in physics is conservation of energy. Therefore, when an electron moves between two stationary Bohr orbits, its energy needs to change. When this transition takes place, energy is either released or absorbed by the atom in form of a photon. The energy released can be calculated using the energy difference between the two stationary orbits. However, it is common to see that potential energy is neglected in such problems as we only include kinetic energy in the equation. Here, we will try to understand why potential energy is ignored in this problem for calculating the energy difference between the two stationary Bohr orbits.
Understanding Bohr’s Model of Atom
Before we get into the topic of why potential energy is ignored in calculating energy difference between two stationary Bohr orbits, let’s first understand the Bohr model of the atom. The Bohr model is one of the earliest atomic models proposed by physicist Niels Bohr. In this model, an electron moves around the positively charged nucleus in circular orbits. Bohr also postulated that electrons could only occupy fixed energy states or stationary orbits.
The fixed energy states or stationary orbits in the Bohr model are determined by the following equation:
Where,
In the Bohr model, an electron can move to another stationary orbit by either absorbing or releasing energy. When energy is absorbed, the electron moves to a higher energy state or stationary orbit. Conversely, when energy is released, the electron moves to a lower energy state or stationary orbit. In either case, the energy absorbed/released can be calculated using the energy difference between the two stationary orbits.
Ignoring Potential Energy in Energy Difference Calculations
Now, let’s return to our original question of why potential energy is neglected when calculating energy difference between two stationary Bohr orbits. The reason for this is that potential energy is a function of the distance between two particles and only the kinetic energy contributes to the energy of the electron that is confined to a fixed orbit in the Bohr model. The potential energy contribution is constant as long as the electron is constrained on the circular orbit. The electron cannot move beyond or approach closer to the nucleus because it can only occupy fixed energy states. Therefore, the potential energy remains constant for both initial and final stationary orbits.
As a result, in problems involving stationary Bohr orbits, we only need to take kinetic energy into account. Kinetic energy is the energy possessed by the electron due to its motion. The kinetic energy of an electron in the Bohr model can be calculated using the following equation:
Where,
When an electron moves from an initial stationary orbit to a final orbit, its kinetic energy changes, and this change in kinetic energy is equal to the energy difference between the two stationary orbits. This energy difference can be calculated using the following equation:
Where,
Once we have calculated the energy difference between the two stationary orbits using the above equation, we can use the equation
to calculate the wavelength of the photon emitted due to the transition of the electron between the two stationary orbits.
Conclusion
In summary, potential energy is ignored in calculating energy difference between two stationary Bohr orbits because it is constant for both initial and final stationary orbits, and therefore does not contribute to the calculation. Only the kinetic energy of the electron changes in a transition between two stationary orbits, and this change in kinetic energy is equal to the energy difference between the initial and final stationary orbits. This energy difference can be used to calculate the wavelength of the photon emitted when an electron undergoes a transition between two stationary Bohr orbits.