When element show transition from n =1 to n= 2 and n=2 to n= 3 thent ( 1) AE and frequency are additive (2) wave length and muency are additive (3) AE_and wavelength are additive _ (4) AE, frequency ahd waveiengtf) afeaddih’ve

To understand the transitions between energy levels in an atom, particularly when an electron moves from one energy level (n=1) to another (n=2 or n=3), we need to consider several key concepts: energy, frequency, and wavelength. Let's break this down step by step.

Energy Levels and Transitions

In an atom, electrons occupy specific energy levels, denoted by quantum numbers (n=1, n=2, n=3, etc.). When an electron transitions from a lower energy level to a higher one, it absorbs energy, and when it falls back to a lower level, it releases energy in the form of electromagnetic radiation.

Understanding Additivity

The question mentions the additivity of various properties during these transitions. Let's clarify what this means:

• Energy (AE) and Frequency: The energy of a photon emitted or absorbed during a transition is directly proportional to its frequency. This relationship is expressed by the equation:

E = h * f

• Where E is energy, h is Planck's constant, and f is frequency. Thus, when an electron transitions between levels, the energy change corresponds to a specific frequency of light.
• Wavelength and Frequency: Wavelength (λ) and frequency are inversely related, as described by the equation:

c = λ * f

• Where c is the speed of light. This means that as the frequency increases, the wavelength decreases. Therefore, if we know the frequency of the emitted or absorbed light, we can find its wavelength.
• Energy, Frequency, and Wavelength: Since energy is related to frequency and frequency is related to wavelength, we can say that energy, frequency, and wavelength are all interconnected. When an electron transitions between energy levels, the energy change can be expressed in terms of both frequency and wavelength.

Practical Example

Let’s consider a hydrogen atom as an example. When an electron transitions from n=1 to n=2, it absorbs energy corresponding to a specific frequency of light. If we calculate the energy difference between these two levels, we can determine the frequency of the photon absorbed. Then, using the speed of light, we can find the wavelength of that photon.

Summary of Relationships

In summary, during the transitions between energy levels:

• The energy change (AE) is directly related to the frequency of the emitted or absorbed light.
• The wavelength is inversely related to the frequency, meaning they are connected through the speed of light.
• Thus, energy, frequency, and wavelength are all part of the same phenomenon, and understanding one helps us understand the others.

So, to answer your question, the correct interpretation is that energy, frequency, and wavelength are all interconnected during these transitions. They are not merely additive in a straightforward sense but rather related through the fundamental equations of physics governing electromagnetic radiation.