Everyday physics applications Questions

Correct Answer

📖 Governing Law / Core Concept

The electromagnetic spectrum includes X-rays, which are characterized by short wavelengths typically in the range of:

🧪 Step-by-Step Breakdown

X-rays are high-energy electromagnetic radiation produced when electrons are decelerated upon striking a metal target:

• For range consideration, X-rays have wavelengths less than visible light, which ranges from approximately 400 nm to 700 nm.
• Therefore, any wavelength above 10 nm does not classify as X-ray.
• Among the options presented:
• A: 500 nm (Visible light)
• B: 5000 nm (Infrared)
• C: 100 nm (Ultraviolet)
• D: 1 nm (X-ray)

🔍 Option Analysis

Analysis of incorrect options:

• A: 500 nm - Falls within the visible spectrum.
• B: 5000 nm - Falls within the infrared spectrum.
• C: 100 nm - While close, it is positioned in the ultraviolet range.

⚡ Mnemonic / Speed-Run

Remember: X-rays are "extremely short", rhyme with "X-rays" and think of a nanometer scale.

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

Cathode rays are streams of electrons observed in vacuum tubes. They travel from the cathode (negative electrode) to the anode (positive electrode).

🧪 Step-by-Step Breakdown

• Definition: Cathode rays are negatively charged particles, primarily electrons.
• Direction of Flow: Electrons move from cathode (−) to anode (+).
• Behavior in Fields: In vacuum, cathode rays travel straight unless influenced by magnetic or electric fields.
• Applications: Used in cathode ray tubes for displays in older television sets.

🔍 Option Analysis

• A: Correct; cathode rays are indeed electrons.
• B: Incorrect; they move from cathode to anode.
• C: True; they travel in straight lines in the absence of fields.
• D: Correct; modern televisions used cathode ray tubes historically.

⚡ Mnemonic / Speed-Run

Remember: "C to A" for Cathode to Anode flow of electrons.

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

The basic scientific principle behind a nuclear reactor is governed by controlled nuclear fission, defined as the process of splitting atomic nuclei in a controlled environment to release energy.

🧪 Step-by-Step Breakdown

In a nuclear reactor, uranium-235 (U-235) or plutonium-239 (Pu-239) undergoes fission when bombarded by neutrons:

This reaction produces additional neutrons which can initiate further fission events, maintaining a controlled chain reaction essential for energy production.

🔍 Option Analysis

- A: Nuclear fusion involves combining light nuclei, not fission.

- B: Controlled nuclear fusion is not feasible with current technology for power generation.

- C: Uncontrolled nuclear fission can lead to catastrophic events (nuclear bombs), unlike reactors that carefully manage the reaction rate.

⚡ Mnemonic / Speed-Run

Remember: Fission = Splitting, Fusion = Combining. Controlled fission is managed energy; uncontrolled is a disaster.

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

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 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

📖 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 categorizes radiation based on wavelength. X-rays occupy the range approximately from \(0.01 \, \text{nm}\) to \(10 \, \text{nm}\).

🧪 Step-by-Step Breakdown

The formula relating energy \(E\) to wavelength \(\lambda\) is given by:

Where:
\(E\) = energy in Joules (J)
\(h\) = Planck's constant \( (6.626 \times 10^{-34} \, \text{J.s}) \)
\(c\) = speed of light \( (3 \times 10^8 \, \text{m/s}) \)
\(\lambda\) = wavelength in meters (m)

Using this, we can estimate energies associated with the options. For instance, at \( \lambda = 1 \, \text{nm} = 1 \times 10^{-9} \, \text{m} \):

This energy is characteristic of X-ray photons.

🔍 Option Analysis

Other options include:

• Option B (10 nm): Also in X-ray range but at the upper threshold.
• Option C (100 nm): Falls into the ultraviolet (UV) spectrum.
• Option D (300 nm): Clearly in the UV spectrum.

⚡ Mnemonic / Speed-Run

Remember: X-ray wavelengths are \(0.01 - 10 \, \text{nm}\). X-rays = eXtreme radiations (short wavelength).

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

X-rays are a form of electromagnetic radiation with wavelengths ranging from 0.01 to 10 nanometers. Unlike radar, which operates on microwaves (wavelengths of 1 mm to 1 m), X-rays are primarily generated when high-energy electrons collide with a metal target, leading to energy emission in the X-ray range.

🧪 Step-by-Step Breakdown

1. Wavelength of X-rays: \[ \text{Typical Wavelength} \approx 1 \, \text{Å} = 1 \times 10^{-10} \text{m} \] 2. Production Mechanism: When high-energy electrons strike a target material (e.g., tungsten), they decelerate rapidly, producing X-ray photons through: \[ \text{Energy} = h \cdot f \] where \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)), and \( f \) is the frequency of the emitted radiation. 3. Distinct from Radar: Radar systems utilize longer wavelengths (microwaves), unsuitable for dispersing X-ray radiation.

🔍 Option Analysis

- Option A: True. X-rays have wavelengths of about 1 Å. - Option B: True. Generated via electron bombardment of metals. - Option C: False. X-rays are not used for radar systems. - Option D: True. X-rays are utilized in cancer treatment, such as radiotherapy.

⚡ Mnemonic / Speed-Run

Remember: X-rays = X-tremely short wavelengths; Radar = Requires longer wavelengths.

6. Visual Suggestion

📖 Factual Verification & Reference

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