Good morning.
We see that

The magnitude(norm, to be precise) can be calculated the following way:

Now the calculus is trivial:
Gay Lussac's Law states: At a constant volume Pressure<span> divided by </span>Temperature<span> is</span>constant<span> P/T = k Together these three laws form the foundation of the Ideal </span>Gas<span>Law. Objective: Students will </span>investigate<span> Gay Lussac's Law relating </span>pressure<span> and</span>temperature<span> at a </span><span>constant temperature.</span>
A. The formula for mean free time is:
t = V/(4π√2 r²vN)
where
N = 1×10¹⁶ molecules (per m³)
V = 1 m³
r = 111×10⁻⁷m (atomic radius of silicon)
Let's solve for v first:
v = √(3RT/M) = √(3(8.314 m³·Pa/mol·K)(25 + 273 K)/28.1 g/mol Si)
v = 16.26 m/s
t = (1 m³)/(4π√2 (111×10⁻⁷m)²(16.26 m/s)(1×10¹⁶ molecules))
<em>t = 2.81×10⁻9 s</em>
<em>Pure silicon has a high resistivity relative to copper because copper is a conductor, while silicon is a semi-conductor. </em>