The velocity of an electron in the second orbit of sodium atom (atomic number =11 ) is v . The velocity of an electron in its fifth orbit will be

Question

The velocity of an electron in the second orbit of sodium atom (atomic number =11 ) is v . The velocity of an electron in its fifth orbit will be (A) v (B)  (22/5)v  (C)  (5/2)  (D)  (2/5)v

Tardigrade Admin · Accepted Answer

Velocity of electron in nth orbit vn=(Z e2/2 ε0 n h) ⇒ v propto (1/n) v1=v, n1=2, n2=5 ∴ (v/v2) =(n2/n1) ∴ (v/v2)=(5/2) ⇒ v2= (2 v/5)

Q. The velocity of an electron in the second orbit of sodium atom (atomic number $= 11$ ) is $v .$ The velocity of an electron in its fifth orbit will be

$v$

$\frac{22}{5} v$

$\frac{5}{2}$

$\frac{2}{5} v$

Velocity of electron in nth orbit
$v_{n} = \frac{Z e ^{2}}{2 ε _{0} nh}$
$\Rightarrow v \propto \frac{1}{n}$
$v_{1} = v, n_{1} = 2, n_{2} = 5$
$∴ \frac{v}{v _{2}} = \frac{n _{2}}{n _{1}}$
$∴ \frac{v}{v _{2}} = \frac{5}{2}$
$\Rightarrow v_{2} = \frac{2 v}{5}$

Q. The velocity of an electron in the second orbit of sodium atom (atomic number =11 ) is v. The velocity of an electron in its fifth orbit will be

v

522​v

25​

52​v

Velocity of electron in nth orbit vn​=2ε0​nhZe2​ ⇒v∝n1​ v1​=v,n1​=2,n2​=5 ∴v2​v​=n1​n2​​ ∴v2​v​=25​ ⇒v2​=52v​

Q. The velocity of an electron in the second orbit of sodium atom (atomic number $= 11$ ) is $v .$ The velocity of an electron in its fifth orbit will be

$v$

$\frac{22}{5} v$

$\frac{5}{2}$

$\frac{2}{5} v$

Velocity of electron in nth orbit
$v_{n} = \frac{Z e ^{2}}{2 ε _{0} nh}$
$\Rightarrow v \propto \frac{1}{n}$
$v_{1} = v, n_{1} = 2, n_{2} = 5$
$∴ \frac{v}{v _{2}} = \frac{n _{2}}{n _{1}}$
$∴ \frac{v}{v _{2}} = \frac{5}{2}$
$\Rightarrow v_{2} = \frac{2 v}{5}$