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### 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.

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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

i. Determine the transition level of electron which emitted photon with wavelength 1280 nm in Paschen series. ii. Calculate the energy change for the formation of the line with the lowest energy in Paschen series.

Learn how to determine the transition level of an electron with photon emission of wavelength 1280 nm in the Paschen series and calculate the energy change for the lowest energy line. This solution involves key physics concepts like the Rydberg formula and photon energy calculations.

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