If $C_{1}$ , $C_{2}$ , $C_{3}$ ........ represent the speeds of $n_{1}$ , $n_{2}$ , $n_{3}$ ........ molecules, then the root mean square speed is.......

$⟮ \frac{n_{1} {C_{1}}^{2} + n_{2} {C_{2}}^{2} + n_{3} {C_{3}}^{2} + . . . . .}{n_{1} + n_{2} + n_{3} + . . . . .} ⟯^{\frac{1}{2}}$

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$\frac{{⟮ n_{1} {C_{1}}^{2} + n_{2} {C_{2}}^{2} + n_{3} {C_{3}}^{2} + . . ⟯}^{\frac{1}{2}}}{n_{1} + n_{2} + n_{3} + . . . . .}$

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$\frac{{⟮ n_{1} {C_{1}}^{2} ⟯}^{\frac{1}{2}}}{n_{1}} + \frac{{⟮ n_{2} {C_{2}}^{2} ⟯}^{\frac{1}{2}}}{n_{2}} + \frac{{⟮ n_{3} {C_{3}}^{2} ⟯}^{\frac{1}{2}}}{n_{3}} + . . . . .$

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$⟮ \frac{{⟮ n_{1} C_{1} + n_{2} C_{2} + n_{3} C_{3} + . . . ⟯}^{2}}{⟮ n_{1} + n_{2} + n_{3} + . . . . . ⟯} ⟯^{\frac{1}{2}}$

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Solution

The correct option is A
$⟮ \frac{n_{1} {C_{1}}^{2} + n_{2} {C_{2}}^{2} + n_{3} {C_{3}}^{2} + . . . . .}{n_{1} + n_{2} + n_{3} + . . . . .} ⟯^{\frac{1}{2}}$

Root mean square speed = $⟮ \frac{n_{1} {C_{1}}^{2} + n_{2} {C_{2}}^{2} + n_{3} {C_{3}}^{2} + . . .}{n_{1} + n_{2} + n_{3} + . . . . .} ⟯^{\frac{1}{2}}$

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Similar questions

If $C_{1}, C_{2}, C_{3}$ .........represent the speeds of $n_{1}, n_{2}, n_{3}$ ......... molecules, then the root mean square speed is _____.

Q. If

C_{1}, C_{2}, C_{3}

.....represent the speeds of

n_{1}, n_{2}, n_{3}

.....molecules, then the root mean square speed is
(a)

{(\frac{n_{1} C_{1}^{2} + n_{2} C_{2}^{2} + n_{3} C_{1}^{3} + \dots}{n_{1} + n_{2} + n_{3} + \dots})}^{\frac{1}{2}}

(b)

\frac{(n_{1} C_{1}^{2} + n_{2} C_{2}^{2} + n_{3} C_{1}^{3} + \dots)^{\frac{1}{2}}}{n_{1} + n_{2} + n_{3} + \dots}

(c)

\frac{(n_{1} C_{1}^{2})^{\frac{1}{2}}}{n_{1}} + \frac{(n_{2} C_{2}^{2})^{\frac{1}{2}}}{n_{2}} + \frac{(n_{3} C_{1}^{3})^{\frac{1}{2}}}{n_{3}} + \dots

(d)

{[\frac{(n_{1} C_{1}^{2} + n_{2} C_{2}^{2} + n_{3} C_{1}^{3} + \dots]^{2}}{(n_{1} + n_{2} + n_{3} + \dots)}]}^{\frac{1}{2}}

Q. If

C_{1}, C_{2}, C_{3}, . . .

represent the speeds of

n_{1}, n_{2}, n_{3}

, .... molecules, then the root mean square speed is:

If $C_{1}, C_{2}, C_{3}$ .........represent the speeds of $n_{1}, n_{2}, n_{3}$ ......... molecules, then the root mean square speed is _____.

Q. Let

5 < n_{1} < n_{2} < n_{3} < n_{4}

be integers such that

n_{1} + n_{2} + n_{3} + n_{4} = 35

. The number of such distinct arrangements

(n_{1}, n_{2}, n_{3}, n_{4})

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If C1,C2,C3........ represent the speeds of n1,n2,n3........ molecules, then the root mean square speed is.......

The correct option is A ⟮n1C12+n2C22+n3C32+.....n1+n2+n3+.....⟯12 Root mean square speed = ⟮n1C12+n2C22+n3C32+...n1+n2+n3+.....⟯12

If $C_{1}$ , $C_{2}$ , $C_{3}$ ........ represent the speeds of $n_{1}$ , $n_{2}$ , $n_{3}$ ........ molecules, then the root mean square speed is.......