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.