We know that $${v_{rms}} = \sqrt {{{3{k_B}T} \over m}} $$. Given, $${k_B} = 1.4 \times {10^{ - 23}}$$ J/K; T = 300 K; m = 7 $$\times$$ 10^$$-$$27 kg. Therefore,

$${v_{rms}} = \sqrt {{{3 \times 1.4 \times {{10}^{ - 23}} \times 300} \over {7 \times {{10}^{ - 27}}}}} $$

$$ = \sqrt {{{3 \times 300 \times 14 \times {{10}^{ - 23}}} \over {7 \times 10 \times {{10}^{ - 27}}}}} $$

$$ = \sqrt {{{{3^2} \times {{10}^2} \times 2 \times {{10}^4}} \over {10}}} = 3 \times 10 \times {10^2} \times \sqrt {{2 \over {10}}} $$

$$ = 3 \times \sqrt {10} \times {10^2} \times \sqrt 2 = 3 \times \sqrt 2 \times \sqrt 5 \times {10^2} \times \sqrt 2 $$

$$ = 3 \times 2 \times \sqrt 5 \times {10^2}$$

$${v_{rms}} = 6 \times {10^2} \times \sqrt 5 = 13.41 \times {10^2}$$ or $${v_{rms}} = 1.34 \times {10^3}$$