In an alternate universe where Rh= 9.9x10-8J. What is the energy change in nanojoules of an electron transitioning from n=5 to n=2.

Formatting:

Do not use scientific notation.
Report to 2 sig figs
Do not include units in your answers. Make sure to report in nanojoules
Make sure your sign is right no points if its wrong.

Question

In an alternate universe where Rh= 9.9x10-8J. What is the energy change in nanojoules of an electron transitioning from n=5 to n=2.

Formatting:

Do not use scientific notation. 
Report to 2 sig figs
Do not include units in your answers. Make sure to report in nanojoules
Make sure your sign is right no points if its wrong.

BlackTom AI · Accepted Answer

The problem uses a hydrogen-like energy level expression with a given Rydberg constant R_H = 9.9e-8 J.

First, write the energy of a level: E_n = -R_H / n^2. Therefore, E_i for n_i = 5 is -R_H / 25, and E_f for n_f = 2 is -R_H / 4.

Next, compute the energy change: ΔE = E_f - E_i = (-R_H / 4) - (-R_H / 25) = -R_H(1/4 - 1/25).

Calculate the bracket: 1/4 = 0.25 and 1/25 = 0.04, so 0.25 - 0.04 = 0.21.

Now multiply by R_H: ΔE = - (9.9e-8 J) × 0.21 = -2.079e-8 J.

Convert to nanojoules: 1 J = 1e9 nJ, so ΔE = -2.079e-8 J × (1e9 nJ / 1 J) = -20.79 nJ.

Rounding to two significant figures gives ΔE ≈ -21 nJ. The negative sign indicates the electron releases energy (a drop in energy).

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