Everyday physics applications

Correct Answer

📖 Governing Law / Core Concept

The relationship between the wavelength (\( \lambda \)) and the frequency (\( f \)) of electromagnetic radiation is given by the equation: where: - \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)), - \( \lambda \) is the wavelength in meters, - \( f \) is the frequency in hertz.

🧪 Step-by-Step Breakdown

For electromagnetic spectrum classification: - Microwaves: \( \lambda \approx 1 \, \text{mm} - 1 \, \text{m} \) - Infra-red: \( \lambda \approx 700 \, \text{nm} - 1 \, \text{mm} \) - Visible light: \( \lambda \approx 400 \, \text{nm} - 700 \, \text{nm} \) - X-rays: \( \lambda \approx 0.01 \, \text{nm} - 10 \, \text{nm} \) Observing the above ranges, it is clear that: \[ \lambda_{X-rays} < \lambda_{Visible} < \lambda_{Infra-red} < \lambda_{Microwaves} \]

🔍 Option Analysis

- **A: Microwaves** - Longer wavelengths, leading to lower frequencies. - **B: Infra-red** - Wavelength range still longer than X-rays. - **C: Visible light** - Wavelength is shorter than microwaves and infra-red but longer than X-rays. - **D: X-rays** - Shortest wavelengths in this range, therefore having the highest frequency.

⚡ Mnemonic / Speed-Run

Remember the mnemonic: **MIV-X** for frequency order: **Microwaves** > **Infra-red** > **Visible** > **X-rays**.

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Core Concept

The energy of a photon is given by the equation E = hf, where \( E \) is energy, \( h \) is Planck's constant, and \( f \) is frequency. The equation reveals that Planck's constant functions as a bridge between energy and frequency and has dimensions equivalent to angular momentum.

🧪 Step-by-Step Breakdown

The dimension analysis begins with:

Given that:

Thus, the dimensions of Planck's constant \( h \) can be derived:

This result corresponds explicitly with the dimensions of angular momentum, which is also expressed as \( [ML^2T^{-1}] \).

🔍 Option Analysis

• Option A: Linear momentum has dimensions of \( [MLT^{-1}] \), which is distinct from those of \( h \).
• Option C: Displacement dimensions are \( [L] \); these do not align with \( h \).
• Option D: Torque dimensions are \( [ML^2T^{-2}] \); these are not equivalent to \( h \).

⚡ Mnemonic / Speed-Run

To recall, remember that Planck's constant \( h \) relates energy to frequency, with dimensions linked to angular momentum denoted as \( [ML^2T^{-1}] \).

📖 Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

The electromagnetic spectrum orders radiation types based on wavelength. The order from shortest to longest wavelength is:

• X-rays
• Ultraviolet
• Infra-red
• Microwaves

🧪 Step-by-Step Breakdown

Radiation types and their approximate wavelength ranges are:

• X-rays: \(10^{-11} \text{ m} \) to \(10^{-8} \text{ m} \)
• Ultraviolet: \(10^{-8} \text{ m} \) to \(10^{-7} \text{ m} \)
• Infra-red: \(10^{-7} \text{ m} \) to \(10^{-4} \text{ m} \)
• Microwaves: \(10^{-4} \text{ m} \) to \(10^{-1} \text{ m} \)

The relation shows that:

🔍 Option Analysis

Options A, B, and D all represent wavelengths shorter than microwaves:

• A: X-rays - shortest wavelength
• B: Ultraviolet - longer than X-rays but shorter than IR
• D: Infra-red - longer than UV but shorter than microwaves

⚡ Mnemonic / Speed-Run

Remember the order: "X-U-IR-M" (X-rays, Ultraviolet, Infra-red, Microwaves) helps to quickly recall increasing wavelength.

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

The discovery of radiation in the late 19th century led to significant advancements in nuclear physics. Marie Curie's work focused on the isolation of radioactive isotopes, specifically Radium, a fundamental element in the understanding of radioactivity.

🧪 Step-by-Step Breakdown

1. **Pairings Evaluation**: - **(1) James Chadwick : Photoelectric effect**: Incorrect. Chadwick discovered the neutron (1932). - **(2) Albert Einstein : Neutron**: Incorrect. Einstein's contribution was in photoelectric effect explanation (1905). - **(3) Marie Curie : Radium**: Correct. Curie discovered radium in 1898. Given the above evaluations, only the third pairing is accurate.

🔍 Option Analysis

- **Option A (1, 2 and 3)**: Incorrect. Two pairs are wrong. - **Option B (1 and 2 only)**: Incorrect. Both listed are wrong. - **Option C (2 and 3 only)**: Incorrect. Only (3) is correct. - **Option D (3 only)**: Correct. Only Curie and Radium is a valid pairing.

⚡ Mnemonic / Speed-Run

Remember "C for Curie, R for Radium." To differentiate correct from incorrect pairs, recall: Chadwick = Neutron, Einstein = Photoelectric.

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

The reaction enabling nuclear energy is governed primarily by the principle of nuclear fission, which is expressed mathematically through Einstein's equation: where \( E \) is the energy released, \( m \) is the mass lost, and \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \, \text{m/s} \)).

🧪 Step-by-Step Breakdown

In nuclear fission, a heavy nucleus (like Uranium-235) absorbs a neutron and becomes unstable. This instability leads to the nucleus splitting into smaller, stable nuclei, releasing energy and additional neutrons in the process: \[ \text{Uranium-235} + \text{neutron} \rightarrow \text{Barium} + \text{Krypton} + 3 \text{neutrons} + \text{energy} \] The energy released during this reaction can be quantified using \( E = mc^2 \), which denotes the conversion of mass to energy.

🔍 Option Analysis

- **Option (b)**: Incorrect. Rutherford's work primarily focused on the discovery of the nucleus, not on fission. - **Option (c)**: Incorrect. Fusion, the process of combining lighter nuclei, was not proposed by Bohr in relation to fission. - **Option (d)**: Incorrect. Heisenberg's contributions centered on quantum mechanics, without specific reference to fusion.

⚡ Mnemonic / Speed-Run

Remember "Fission Flares" for nuclear fission and "E=mc²" for energy-mass equivalence.

📖 Factual Verification & Reference