Question

this energy diagram shows the allowed energy levels of an electron in a certain atom. (note: the si prefix zepto means $10^{-21}$ any si prefix in the aleks data tab.)
energy (zj)
diagram with energy levels a, b, c (a at ~400 zj, b at ~800 zj, c at ~1000 zj) and a red arrow from a to c
use this diagram to complete the table below.

if the electron makes the transition shown by the red arrow, from a to c, calculate the wavelength of the photon that would be absorbed or emitted. round your answer to 3 significant digits.	\\(\boxed{\text{nm}}\\)

buttons for input adjustment

Explanation:

Step1: Determine energy difference

From the diagram, energy of A ($E_A$) is 400 zJ, energy of C ($E_C$) is 1000 zJ. Energy difference $\Delta E = E_C - E_A = 1000 - 400 = 600$ zJ. Convert zJ to J: $1$ zJ = $10^{-21}$ J, so $\Delta E = 600 \times 10^{-21}$ J = $6 \times 10^{-19}$ J.

Step2: Use photon energy formula

Photon energy $E = h
u = \frac{hc}{\lambda}$, where $h = 6.626 \times 10^{-34}$ J·s, $c = 3.00 \times 10^8$ m/s. Solve for $\lambda$: $\lambda = \frac{hc}{\Delta E}$.

Step3: Calculate wavelength

Substitute values: $\lambda = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{6 \times 10^{-19}}$. Calculate numerator: $(6.626 \times 3.00) \times 10^{-34 + 8} = 19.878 \times 10^{-26} = 1.9878 \times 10^{-25}$. Divide by $6 \times 10^{-19}$: $\lambda = \frac{1.9878 \times 10^{-25}}{6 \times 10^{-19}} = 3.313 \times 10^{-7}$ m. Convert to nm: $1$ m = $10^9$ nm, so $\lambda = 3.313 \times 10^{-7} \times 10^9 = 331.3$ nm, round to 3 sig figs: 331 nm.

Answer:

331