\(\left|V_{\text {rel }}\right|=\sqrt{V^{2}+V^{2}-2(V)(V) \cos \theta}\)

\(=2 V\left|\sin \frac{\theta}{2}\right|\)

This implies,

\(\left\langle V_{\text {rel }}\right\rangle=\frac{\int_{0}^{\pi} 2 V\left|\sin \frac{\theta}{2}\right| d \theta}{\int_{0}^{\pi} d \theta}\)

\(=\frac{4 V}{\pi}\)

Thus,

\(\left\langle V_{\text {га }}\right\rangle=\frac{4}{\pi} V_{\text {average}}\)

\(=\frac{4}{\pi} \sqrt{\frac{8 R T}{\pi m_{0}}}\) \(....(I)\)

Substitute the values in equation \((I).\)

\(\left\langle V_{\text {гel }}\right\rangle=\frac{4}{\pi} \sqrt{\frac{8 \times 8.3 \times 300}{3.14 \times 28 \times 10^{-3}}}\)

\(=606 \,m / sec\)