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To calculate the energy difference between two energy levels in an atom, we can use the formula:

ΔE = hc / λ

Where: ΔE is the energy difference h is Planck's constant (approximately 6.626 x 10^(-34) J·s) c is the speed of light (approximately 2.998 x 10^8 m/s) λ is the wavelength of the emitted light

Let's calculate the energy difference using the given wavelength of 589 nm:

First, convert the wavelength to meters: λ = 589 nm = 589 x 10^(-9) m

Now we can substitute the values into the formula:

ΔE = (6.626 x 10^(-34) J·s * 2.998 x 10^8 m/s) / (589 x 10^(-9) m)

Simplifying the expression:

ΔE = (1.975 x 10^(-25) J·m) / (589 x 10^(-9) m)

Dividing the numerator by the denominator:

ΔE ≈ 3.35 x 10^(-19) J

Therefore, the energy difference between the energy levels in the sodium atom, corresponding to emitted light with a wavelength of 589 nm, is approximately 3.35 x 10^(-19) joules.

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