Question

For each of the questions, four choices have been provided. Select the correct alternative. The difference in energy of radiation emitted (or) absorbed during electronic transition is (a) directly proportional to frequency (b) directly proportional to wavelength (c) inversely proportional to frequency (d) inversely proportional to velocity of light

Short answer

Answer: (a) directly proportional to frequency

Step-by-step solution

Planck's equation

Recall the Planck's equation: E = h * f, where E is the energy of radiation, h is the Planck constant, and f is the frequency of radiation. From this equation, we can see that the energy is directly proportional to the frequency.

Frequency and wavelength relationship

Recall the equation relating frequency (f) and wavelength (λ): c = λ * f, where c is the speed of light. We can rewrite this equation to find the frequency of radiation: f = c / λ.

Substitute the frequency in the Planck's equation

Using the relationship from Step 2, substitute the frequency (f) in the Planck's equation: E = h * (c / λ). This equation shows that the energy is inversely proportional to the wavelength.

Select the correct alternative

Based on Steps 1 and 3, the energy of radiation emitted or absorbed during electronic transitions is directly proportional to the frequency and inversely proportional to the wavelength. Thus, the correct alternative is (a) directly proportional to frequency.

Key concepts

Planck's equation

The energy of radiation involved in electronic transitions is addressed using Planck's equation. This equation is a fundamental principle in quantum mechanics and it connects energy (\(E\)) to frequency (\(f\)) through the Planck constant (\(h\)): \[E = h \cdot f\].
Notably, Planck's equation shows that energy is directly proportional to frequency. This means, as the frequency increases, the energy increases, and vice versa.

• Planck Constant: A universal constant with a value of \(6.626 x 10^{-34} \) Joule-seconds.
• Frequency: The number of wave cycles passing a point per unit time, often measured in Hertz (Hz).

Understanding this relationship helps explain why higher frequency radiation (like ultraviolet light) carries more energy than lower frequency radiation (like radio waves).

Frequency and wavelength relationship

Another key relationship in understanding radiation energy deals with frequency and wavelength. It's essential to recognize how these two properties are linked through the speed of light (\(c\)) with the formula: \( c = \lambda \cdot f \).
Here, \(\lambda\) is the wavelength, representing the distance between consecutive peaks of a wave.

• Wavelength (\(\lambda\)): Measured in meters (m), dictates how stretched out or compressed a wave is.
• Speed of Light (\(c\)): A constant with a value of \(3.00 \times 10^8\) m/s, denoting how fast light travels in a vacuum.

We can rearrange the equation to solve for frequency: \(f = \frac{c}{\lambda}\).
This equation demonstrates that frequency and wavelength have an inverse relationship. When the wavelength is shorter, the frequency is higher, resulting in higher energy as per Planck's equation.

Radiation emission and absorption

When examining electronic transitions in atoms or molecules, the processes of radiation emission and absorption become crucial.

• Emission: Occurs when an electron falls to a lower energy level, releasing energy typically as light or other electromagnetic radiation.
• Absorption: Happens when an electron gains energy, moving to a higher energy level by absorbing a photon.

The energy difference during these transitions (\(\Delta E\)) correlates with the frequency and wavelength of the radiation, as defined by Planck's equation and the frequency-wavelength relationship.
It's essential to realize:- Energy is directly proportional to frequency.- Energy is inversely proportional to wavelength. This understanding allows us to predict the color and energy of light emitted or absorbed during transitions, crucial for fields like spectroscopy and quantum chemistry.