Question 427: Thermodynamics & KTG

Question

The value closest to the thermal velocity of a Helium atom at room temperature (300 K)  in ms
-1
is :
[k
B
=1.4 $$ 	imes $$ 10
-23
J/K; m
He
= 7 $$ 	imes $$ 10
-27
kg ]

Accepted Answer

We know that $${v_{rms}} = \sqrt {{{3{k_B}T} \over m}} $$. Given, $${k_B} = 1.4 	imes {10^{ - 23}}$$ J/K; T = 300 K; m = 7 $$	imes$$ 10
$$-$$27
kg. Therefore,
$${v_{rms}} = \sqrt {{{3 	imes 1.4 	imes {{10}^{ - 23}} 	imes 300} \over {7 	imes {{10}^{ - 27}}}}} $$
$$ = \sqrt {{{3 	imes 300 	imes 14 	imes {{10}^{ - 23}}} \over {7 	imes 10 	imes {{10}^{ - 27}}}}} $$
$$ = \sqrt {{{{3^2} 	imes {{10}^2} 	imes 2 	imes {{10}^4}} \over {10}}}  = 3 	imes 10 	imes {10^2} 	imes \sqrt {{2 \over {10}}} $$
$$ = 3 	imes \sqrt {10}  	imes {10^2} 	imes \sqrt 2  = 3 	imes \sqrt 2  	imes \sqrt 5  	imes {10^2} 	imes \sqrt 2 $$
$$ = 3 	imes 2 	imes \sqrt 5  	imes {10^2}$$
$${v_{rms}} = 6 	imes {10^2} 	imes \sqrt 5  = 13.41 	imes {10^2}$$ or $${v_{rms}} = 1.34 	imes {10^3}$$

Answer

1.3 $$ 	imes $$ 10
4

Answer

1.3 $$ 	imes $$ 10
3

Answer

1.3 $$ 	imes $$ 10
5

Answer

1.3 $$ 	imes $$ 10
2

Thermodynamics & KTG

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms -1 is : [k B =1.4 $ \times 10 -23 J/K; m He = 7 \times $ 10 -27 kg ]

Choose the correct answer: