Let's break down the problem based on the image you've provided:

Part (i): Determine the transition level of the electron which emitted a photon with a wavelength of 1280 nm in the Paschen series.

Solution: The Paschen series corresponds to transitions where the final energy level (n₂) is 3. The wavelength of the photon can be related to the energy difference between two energy levels using the Rydberg formula for hydrogen:

$\frac{1}{\lambda} = R_H \left( \frac{1}{n_2^2} - \frac{1}{n_1^2} \right)$

where:

• $\lambda$ is the wavelength (1280 nm),
• $R_H$ is the Rydberg constant ($1.097 \times 10^7 \, \text{m}^{-1}$),
• $n_2 = 3$ for the Paschen series (final state),
• $n_1$ is the initial energy level (to be determined).

Rewriting the formula to solve for $n_1$, we get:

$\frac{1}{n_1^2} = \frac{1}{n_2^2} - \frac{1}{R_H \lambda}$

We will substitute the values and solve for $n_1$.

Part (ii): Calculate the energy change for the formation of the line with the lowest energy in the Paschen series.

Solution: The lowest energy line in the Paschen series corresponds to the transition from $n_1 = 4$ to $n_2 = 3$. The energy difference is given by the formula:

$E = h \cdot c \cdot \left( \frac{1}{n_2^2} - \frac{1}{n_1^2} \right)$

where:

• $h$ is Planck’s constant ($6.626 \times 10^{-34} \, \text{J·s}$),
• $c$ is the speed of light ($3.0 \times 10^8 \, \text{m/s}$),
• $n_1 = 4$ and $n_2 = 3$.

We will calculate this energy in joules.

Let me proceed with the calculations.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can guide you through the calculations step-by-step to solve these problems manually. Let me know if you'd like to proceed that way or have any other questions!

Here are some related questions for practice:

1. What is the significance of the Rydberg constant in atomic physics?
2. How does the Paschen series differ from the Balmer and Lyman series in terms of electron transitions?
3. What factors influence the energy change during electron transitions in hydrogen atoms?
4. How can we derive the energy of a photon from its wavelength?
5. Why does