Calculate Change in Energy for n=4 to n=1 Hydrogen Atom

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The change in energy for the transition from n=4 to n=1 in a hydrogen atom is calculated using the formula E = -Rh(1/n(low)^2 - 1/n(high)^2). The correct answer for this transition is -2.04E-18J, indicating that energy is released when the electron moves to a lower energy level. Confusion arises from differing interpretations of the sign of the energy change, with some sources suggesting it could be positive. However, the negative sign reflects that energy is lost by the atom and gained by the surroundings. Ultimately, the sign of the change in energy depends on the perspective of the system versus its environment.
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Calculate the change in energy when the following transition occurs in the hydrogen atom.

n = 4 ----> n = 1

equation

E = -Rh/n^2

eventually my answer is 2.04E-18J because my book tells me to take 1 over n(low) squared minus 1over n(high) squared and multiply by rydberg constant.. so doing it according to the book i get a positive number

but the answer is -2.04E-18J... and now after looking online... I am getting serveral mixed sources, some saying that it is positive, others saying it is negative.. which is it.
 
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Negative.
 
This is change in energy. Whatever atom loses is gained by surroundings, so sign if the change is either negative or positive, depending on the point of view.

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