Use an unambiguous diagram to illustrate how a beam of radiation is attenuated by an absorbing substance, and define the terms Pt and Po. Also illustrate how an atom with two different energy levels i

2. (a) Use an unambiguous diagram to illustrate how a beam of radiation is attenuated by an absorbing substance, and define the terms $P_t$ and $P_o$.

• Diagram Description: Imagine a light source emitting a beam of radiation. This beam, with initial radiant power $P_o$, travels towards a sample cell containing an absorbing substance. As the beam passes through the substance, some of its energy is absorbed. The remaining radiation, with reduced radiant power $P_t$, exits the sample cell and is detected.

  $$\text{Incident Beam } (P_o) \quad \longrightarrow \quad \boxed{\text{Absorbing Substance}} \quad \longrightarrow \quad \text{Transmitted Beam } (P_t)$$

• Definitions:

  • $P_o$: The incident radiant power (or intensity) of the light beam before it enters the absorbing substance.
  • $P_t$: The transmitted radiant power (or intensity) of the light beam after it has passed through the absorbing substance.

2. (b) Illustrate how an atom with two different energy levels is separated.

• Diagram Description: An atom typically exists in a lower energy state, called the ground state ($E_1$). When it absorbs a photon of specific energy, it can transition to a higher energy state, called an excited state ($E_2$). The energy difference between these two levels, $\Delta E = E_2 - E_1$, corresponds to the energy of the absorbed photon.

  $$\text{Excited State } (E_2)$$ $$\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \uparrow \text{ Absorption of photon}$$ $$\text{Ground State } (E_1)$$

2. (c) Write an equation which relates the photon to frequency, wavelength and wave number.

The energy ($E$) of a photon is related to its frequency ($\nu$), wavelength ($\lambda$), and wavenumber ($\bar{\nu}$) by the following equation:

$$E = h\nu = \frac{hc}{\lambda} = hc\bar{\nu}$$

where $h$ is Planck's constant and $c$ is the speed of light.

2. (d) How does the quantum theory describe light?

Quantum theory describes light as consisting of discrete packets of energy called photons. Each photon has a specific, quantized amount of energy, $E = h\nu$, where $\nu$ is its frequency. This theory also posits that light exhibits wave-particle duality, meaning it can behave as both a wave (demonstrating phenomena like diffraction and interference) and a particle (interacting as discrete energy packets).

2. (e) Mention two major differences between IR spectrum and UV-Visible spectrum.

• Type of Transitions:
  • IR spectroscopy primarily involves vibrational and rotational transitions within molecules.
  • UV-Visible spectroscopy involves electronic transitions, where electrons move between different energy orbitals.
• Energy and Wavelength Range:
  • IR spectroscopy uses lower energy, longer wavelength infrared radiation (typically $2.5 \text{ to } 25 \text{ µm}$).
  • UV-Visible spectroscopy uses higher energy, shorter wavelength ultraviolet and visible radiation (typically $200 \text{ to } 800 \text{ nm}$).

2. (f) Explain the function of the beam splitter in a Michelson interferometer.

The function of a beam splitter in a Michelson interferometer is to divide an incoming beam of light into two separate beams. It is typically a partially silvered mirror that allows a portion of the light to pass through (transmitted beam) and reflects the remaining portion (reflected beam). These two beams then travel different optical paths and are subsequently recombined by the same beam splitter, creating an interference pattern that can be analyzed.