The mean free path of a molecule of He gas is α. Its mean free path along any arbitrary coordinate axis will be

Question

The mean free path of a molecule of He gas is α. Its mean free path along any arbitrary coordinate axis will be (A) α (B) (α/3) (C) (α/√3) (D) 3 α

Tardigrade Admin · Accepted Answer

Mean free path of a molecule is the resultant of path along three separate axis and they will be equal. So, α=√αx2+αy2+α22 where αx=αy2 α2= (say) a α=√a2+a2+a2 or a=(α/√3)

Q. The mean free path of a molecule of $He$ gas is $α$ . Its mean free path along any arbitrary coordinate axis will be

$α$

$\frac{α}{3}$

$\frac{α}{3}$

$3 α$

Mean free path of a molecule is the resultant of path along three separate axis and they will be equal.
So, $α = α_{x}^{2} + α_{y}^{2} + α_{2}^{2}$
where $α_{x} = α_{y}^{2} α_{2} =$ (say) $a$
$α = a^{2} + a^{2} + a^{2}$
or $a = \frac{α}{3}$

Q. The mean free path of a molecule of He gas is α. Its mean free path along any arbitrary coordinate axis will be

α

3α​

3​α​

3α

Mean free path of a molecule is the resultant of path along three separate axis and they will be equal. So, α=αx2​+αy2​+α22​​ where αx​=αy2​α2​= (say) a α=a2+a2+a2​ or a=3​α​

Q. The mean free path of a molecule of $He$ gas is $α$ . Its mean free path along any arbitrary coordinate axis will be

$α$

$\frac{α}{3}$

$\frac{α}{3}$

$3 α$

Mean free path of a molecule is the resultant of path along three separate axis and they will be equal.
So, $α = α_{x}^{2} + α_{y}^{2} + α_{2}^{2}$
where $α_{x} = α_{y}^{2} α_{2} =$ (say) $a$
$α = a^{2} + a^{2} + a^{2}$
or $a = \frac{α}{3}$