Hydrogen Spectrum and Electron Transitions

The hydrogen spectrum refers to the collection of electromagnetic radiation emitted or absorbed by hydrogen atoms when their electrons undergo transitions between different energy levels. These transitions occur when the electrons gain or lose energy, causing them to move between different orbits or energy levels. Each transition is associated with a specific wavelength or color of light.

Electron Transition from Orbit 7 to 1 in Multiple Steps

In the given scenario, the electron in a hydrogen atom is transitioning from the 7th orbit to the 1st orbit. However, it is stated that this transition occurs in multiple steps. This means that the electron does not directly jump from the 7th to the 1st orbit, but rather goes through intermediate orbits.

Calculating the Total Number of Lines in the Spectrum

To determine the total number of lines in the spectrum, we need to consider the number of intermediate orbits the electron passes through during the transition from orbit 7 to 1.

Energy Levels in Hydrogen Atom
In a hydrogen atom, the energy levels are quantized, meaning they can only have certain specific values. The energy levels are given by the formula:

En = -13.6 eV/n^2

where En is the energy level, n is the principal quantum number, and -13.6 eV is the ionization energy of hydrogen.

Calculating Energy Difference between Orbits
To move from one orbit to another, the electron must either absorb or emit energy equal to the difference in energy between the two orbits. The energy difference (∆E) between two energy levels can be calculated using the formula:

∆E = Ef - Ei

where Ef is the final energy level and Ei is the initial energy level.

Number of Steps and Lines
By calculating the energy difference between each pair of consecutive orbits, we can determine the number of steps the electron takes and the associated number of lines in the spectrum.

For example, to move from the 7th orbit to the 6th orbit, the electron must emit energy equal to the difference between the energy levels of these orbits. Similarly, to move from the 6th to the 5th orbit, another energy difference needs to be emitted. This process continues until the electron reaches the 1st orbit.

Each energy difference corresponds to a specific wavelength or color of light, resulting in the emission or absorption of a line in the spectrum.

Conclusion
To find the total number of lines in the spectrum when an electron moves from the 7th to the 1st orbit in multiple steps, we need to calculate the energy differences between each pair of consecutive orbits. Each energy difference corresponds to a specific line in the spectrum. By summing up the number of lines emitted or absorbed in each step, we can determine the total number of lines in the hydrogen spectrum.