Which of the following transition in a hydrogen atom emits a photon of highest frequency ?

To determine which transition in a hydrogen atom emits a photon of the highest frequency, we need to consider the energy levels of the hydrogen atom and the relationship between energy and frequency. The frequency of a photon emitted during a transition is directly related to the energy difference between the two levels involved in that transition.

Understanding Energy Levels in Hydrogen

The hydrogen atom has quantized energy levels, which can be described by the formula:

E_n = -13.6 eV / n²

Here, E_n is the energy of the level, and n is the principal quantum number (n = 1, 2, 3, ...). The ground state corresponds to n = 1, and as n increases, the energy levels become less negative, indicating that the electron is further from the nucleus.

Photon Emission and Frequency

When an electron transitions from a higher energy level (n_i) to a lower energy level (n_f), it emits a photon. The energy of the emitted photon can be calculated using:

E_photon = E_n(i) - E_n(f)

According to Planck's equation, the frequency (ν) of the emitted photon is related to its energy by:

E_photon = hν

Where h is Planck's constant (approximately 6.626 x 10^-34 J·s). Thus, the frequency can be expressed as:

ν = E_photon / h

Identifying the Highest Frequency Transition

To find the transition that emits the highest frequency photon, we should look for the transition with the largest energy difference. The largest energy difference occurs when an electron falls from the highest possible energy level to the lowest energy level (n = 1).

• Transition from n = 2 to n = 1
• Transition from n = 3 to n = 1
• Transition from n = 4 to n = 1
• Transition from n = 5 to n = 1

The transition from n = 2 to n = 1 has a smaller energy difference compared to the transition from n = 3 to n = 1, and so on. Therefore, the transition from n = ∞ (the highest level) to n = 1 will yield the highest frequency photon.

Final Thoughts

In summary, the transition that emits a photon of the highest frequency in a hydrogen atom is the one where the electron transitions from the highest energy level (n = ∞) to the ground state (n = 1). This transition results in the maximum energy difference, and consequently, the highest frequency photon is emitted.