In a research laboratory, scientists are studying the distribution of particle velocities in a gas sample. The distribution function 𝑓(𝑣) for the velocity 𝑣 of particles is given by the Maxwell-Boltzmann distribution $f(v)=4 \pi N\left(\frac{m}{2 \pi k T}\right)^{3 / 2} v^{2} e^{-\frac{m v^{2}}{2 k T}}$ . Using this distribution function, calculate the value of the integral $\int_{0}^{\infty} f(v) d v$.

• A. $\frac{N}{4}$
• B. $\frac{N}{2}$
• C. $N$
• D. $2N$