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In the question in the lecture where the question is asking to calculate the frequency of light emitted by a hydrogen atom when an electron transitions from the 4th to the second, I am a little confused on why the sign for the energy changed from negative to positive when we plugged it in to the E=hv equation. Does anyone know why this is?
The sign become opposite because in the E=hv equation we switch to talking about the photon which is equal and opposite to the negative electron. The electron we had been using for the first part of the calculations which was negative because it was emitting or losing energy to the photon, which was gaining energy.
The negative when finding the difference in energy just shows that energy decreased and it was released as electromagnetic radiation, since there is no such thing as negative energy, so when using the E=hv formula, you take away the negative
When you find the change in energy when an electron moves to a lower energy level, it is negative because the resulting energy will be lower than the initial energy. However when you are finding the energy emitted, it will be positive. This is the energy released as light when the electron moves to a lower energy level. Due to the principle of conservation of energy, the emitted energy value will be equal and opposite to the negative energy value.
The sign for the energy switched from negative to positive because the first calculations gave us the energy lost by the electron as it transitioned between the levels. The sign for this energy is negative because the energy was lost. The sign for the energy then switched to positive because we were then dealing with the energy gained by the photon, which is equal and opposite to the energy lost by the electron.
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