Electric Conductivity

Step 1: Understanding the relationship between conductivity and temperature.
In most metals, as temperature increases, the conductivity decreases due to increased lattice vibrations which scatter electrons. This results in a negative temperature coefficient of resistance. The graph that best represents this relationship is a decreasing curve, corresponding to option (B).
Step 2: Conclusion.
Thus, the correct answer is option (B) because conductivity decreases with increasing temperature in metals.

Step 1: Understanding the relationship between conductivity and temperature.
In most metals, as temperature increases, the conductivity decreases due to increased lattice vibrations which scatter electrons. This results in a negative temperature coefficient of resistance. The graph that best represents this relationship is a decreasing curve, corresponding to option (A).
Step 2: Conclusion.
Thus, the correct answer is option (A) because conductivity decreases with increasing temperature in metals.

Step 1: Understanding the relationship between electron concentration and temperature.
The electron concentration in a semiconductor follows an exponential dependence on temperature, described by the equation: where is the electron concentration at a reference temperature, is the band gap, is Boltzmann's constant, and is the temperature. The electron concentration at 300 K is given as . This means we can calculate the value of at 200 K using the exponential model for temperature dependence.
Step 2: Deriving the exponential model.
The electron concentration at 200 K, , is related to the electron concentration at 300 K, , as follows: Taking the ratio of these two equations gives: Substitute the given band gap value of and simplify the equation to find the ratio.
Step 3: Conclusion.
By solving the equation, we find that the value of is 3, so the correct answer is .