Question

Statement 1: The drift speed of electrons in metals is small (in order of few mm/sec ) and the charge of an electron is also very small $\left( 1\cdot 6\times {{10}^{-19}}\text{C} \right)$ , yet we can obtain a large current in a metal.
Statement 2: At room temperature, the thermal speed of electrons is very high (about ${{10}^{7}}$ times the drift speed).
A. Statement 1 is true. Statement 2 is true. Statement 2 is the correct explanation of statement 1.
B. Statement 1 is true. Statement 2 is true statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true, statement 2 is false.
D. Statement 1 is false, Statement 2 is true

Answer 1

The equation for current is a conductor is I = ne A $v_d$
Here we can see that the current is dependent on drift velocity and thermal velocity. SO, from here, we can figure out whether statement 2 is the correct explanation of statement 1 or not.

Complete step by step solution:
The correct explanation of statement 1 is as follows:
We know that the current in a conductor is given by the equation
I = ne A $v_d$
Where n= number density of free electrons
e = charge of electrons
a = area of cross-section of conductor
$v_d$ = drift velocity.
Number density means the number of particles that are present in a particular volume.
Now, the conductors have a large number density of free electrons (around ${{10}^{28}}\text{ per c}{{\text{m}}^{3}}$ ). These are responsible for electric current flow in a conductor. That’s why we obtain large current in a conductor.
So, statement 2 is true but not a correct explanation of statement 1

Note: Drift velocity is the net velocity of electrons in a particular direction under an applied field. The thermal velocity has no net direction because it is randomly distributed and occurs in any metal at finite temperature. Thermal velocity is due to thermal agitation.
At room temperature the atoms are agitated, they vibrate more leading to more collisions on the way and hence drift velocity decreases.