Band Theory Of Solids

Step 1: Concept
p-type (positive-type) semiconductors are created by doping with trivalent impurities.
Step 2: Analysis
Trivalent impurities create "vacancies" or "holes" in the crystal lattice.
Step 3: Conclusion
Holes are the majority carriers in p-type, while electrons are the majority in n-type.
Final Answer: (B)

Step 1: Permutation Concept
A tripeptide is formed by linking three amino acids together.
Step 2: Calculation
Since there are 20 options for each of the three positions in the tripeptide chain, we use the formula where is the number of amino acids and is the length of the peptide.
Step 3: Result
Number of possible tripeptides .
Final Answer: (a)

Step 1: Understanding the energy gap in insulators.
In insulators, the energy gap between the valence band (where electrons are bound to the atoms) and the conduction band (where electrons can move freely) is significantly wide. This wide gap prevents electrons from easily moving into the conduction band under normal conditions.

Step 2: Size of the energy gap.
For insulators, the energy gap is typically much larger than that in semiconductors, which typically have energy gaps around 1.1 eV. For insulators like diamond or glass, the energy gap is usually around 5 eV or more. This large gap results in the inability of electrons to jump to the conduction band at room temperature.

Step 3: Conclusion.
The energy gap between the valence and conduction bands in an insulator is typically around 5.0 eV, which prevents electrical conduction.

Step 1: Understanding the energy gap in semiconductors.
In semiconductors, the forbidden energy gap is the energy difference between the valence band and the conduction band. For germanium, this gap is well known and can be calculated using the following relation for the energy gap in terms of temperature and material properties.

Step 2: Use the known value for germanium.
The forbidden energy gap for germanium at room temperature is typically around , which corresponds to the value given in option (1).

Step 3: Conclusion.
The correct answer is , which is option (1).

Step 1: Use the energy-wavelength relation.
The energy of a photon is related to its wavelength by the formula: where: - is Planck's constant ( ), - is the speed of light ( ), - is the wavelength.

Step 2: Apply the given values.
We are given that the energy required to create a hole is . We need to convert this to Joules:

Step 3: Solve for the wavelength.
Rearranging the energy-wavelength formula: Substitute the values:

Step 1: Understanding the Concept:
KE = . Let mass of man = , boy = .
Step 2: Detailed Explanation:
Initial: . But .
.
After speed up: .
.
Step 3: Final Answer:
Thus, original speed = .

Step 1: Understanding the Concept:
Using Gauss's law in terms of solid angle, total flux associated with a charge can be expressed including angular factor .
Step 2: Detailed Explanation:
Total flux = .
Since the cube has 6 faces and symmetry applies, flux through each face = .
Step 3: Final Answer:
Thus, flux through any face = .

Step 1: Understanding the Concept:
Resultant velocity across river = width/time. Also, .
Step 2: Detailed Explanation:
Width = 320 m, time = 4 min. Velocity across river = m/min.
Let current speed = . Man's speed in still water = .
To cross perpendicularly, (vector addition: man swims at angle upstream).
.
m/min.
Step 3: Final Answer:
Thus, speed of current = 60 m/min.

Concept: In semiconductors, electrons are bound in covalent bonds. To free an electron for conduction, energy equal to the band gap (forbidden energy gap) must be supplied.

Step 1: Understand bond breaking.
Breaking a covalent bond means promoting an electron from the valence band to the conduction band.

Step 2: Relate to energy gap.
The minimum energy required is exactly the forbidden energy gap .

Concept: This famous observation is known as Moore's Law.

Step 1: Identify the scientist. Gordon Moore, co-founder of Intel, observed in 1965 that the number of transistors per square inch on integrated circuits doubles approximately every year (later revised to every two years).

Step 2: Other options.
• Alan Turing: Father of theoretical computer science, Turing machine.
• John von Neumann: Von Neumann architecture.
• Herbert Simon: Nobel laureate in economics, artificial intelligence.