The visible spectrum of light emitted by a star is observed to contain a number of dark lines - Scottish Highers Physics - Question 6 - 2017

To find the frequency of the photon absorbed during the transition from E₁ to E₃, we first calculate the change in energy (ΔE):

$$ΔE = E₃ - E₁ = (-1.36 imes 10^{-19} J) - (-5.42 imes 10^{-19} J) = 4.06 imes 10^{-19} J$$

Next, we use the formula relating energy and frequency:

$$E = hf$$

Where:

• $E$ is the energy of the photon,
• $h$ is Planck's constant ($6.63 imes 10^{-34} Js$), and
• $f$ is the frequency.

Thus, we rearrange to find frequency:

$$f = \frac{E}{h} = \frac{4.06 imes 10^{-19} J}{6.63 imes 10^{-34} Js} \approx 6.13 \times 10^{14} Hz$$

Therefore, the frequency of the photon absorbed is approximately $6.13 \times 10^{14} Hz$.