The number of molecules per unit volume of a gas depends on their distance r from the origin as, n(.r.)=n0e- α r4 , where n0 and α are constants.The total number of molecules of the gas is proportional to:

Question

The number of molecules per unit volume of a gas depends on their distance r from the origin as, n(.r.)=n0e- α r4 , where n0 and α are constants.The total number of molecules of the gas is proportional to: (A)  n0α 1 / 4 (B) n0α - 3 / 4 (C) n0α - 3 (D)  √n0α 1 / 2

Tardigrade Admin · Accepted Answer

The number density or number of molecules per unit volume is given by equation

n (r) = n_{0} e^{- α r^{4}}

. Then, the total number of the molecule will be given by,

Total molecule N = \int_{0}^{\infty} n (r) (4 π r^{2} d r)

N = \int_{0}^{\infty} 4 π n_{0} e^{- α r^{4}} r^{2} d r

After integration,

N \propto n_{0} α^{- 3/4}

.

Q. The number of molecules per unit volume of a gas depends on their distance r from the origin as, $n (r) = n_{0} e^{- α r^{4}}$ , where $n_{0}$ and $α$ are constants.The total number of molecules of the gas is proportional to:

$n_{0} α^{1/4}$

$n_{0} α^{- 3/4}$

$n_{0} α^{- 3}$

$n_{0} α^{1/2}$

Q. The number of molecules per unit volume of a gas depends on their distance r from the origin as, n(r)=n0​e−αr4 , where n0​ and α are constants.The total number of molecules of the gas is proportional to:

n0​α1/4

n0​α−3/4

n0​α−3

n0​​α1/2

The number density or number of molecules per unit volume is given by equation n(r)=n0​e−αr4 . Then, the total number of the molecule will be given by, Total molecule N=∫0∞​n(r)(4πr2dr) N=∫0∞​4πn0​e−αr4r2dr After integration, N∝n0​α−3/4 .

Q. The number of molecules per unit volume of a gas depends on their distance r from the origin as, $n (r) = n_{0} e^{- α r^{4}}$ , where $n_{0}$ and $α$ are constants.The total number of molecules of the gas is proportional to:

$n_{0} α^{1/4}$

$n_{0} α^{- 3/4}$

$n_{0} α^{- 3}$

$n_{0} α^{1/2}$