The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to nx , where x is

Question

The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to nx , where x is (A) 0 (B) 1 (C) -2 (D) 2

Tardigrade Admin · Accepted Answer

Linear momentum = mv = (m c Z/137 n) Angular momentum = (n h/2 π ) Given, Linear momentum × angular momentum propto nx ∴ (m c Z/137 n) × (n h/2 π ) propto nx n0 propto nx ⇒ x=0

Q. The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to $n^{x}$ , where $x$ is

$0$

$1$

$- 2$

$2$

Linear momentum = $m v = \frac{m c Z}{137 n}$
Angular momentum = $\frac{nh}{2 π}$
Given,
Linear momentum $\times$ angular momentum $\propto n^{x}$
$∴ \frac{m c Z}{137 n} \times \frac{nh}{2 π} \propto n^{x}$
$n^{0} \propto n^{x}$
$\Rightarrow x = 0$

Q. The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to nx , where x is

0

1

−2

2

Linear momentum = mv=137nmcZ​ Angular momentum = 2πnh​ Given, Linear momentum × angular momentum ∝nx ∴137nmcZ​×2πnh​∝nx n0∝nx ⇒x=0

Q. The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to $n^{x}$ , where $x$ is

$0$

$1$

$- 2$

$2$

Linear momentum = $m v = \frac{m c Z}{137 n}$
Angular momentum = $\frac{nh}{2 π}$
Given,
Linear momentum $\times$ angular momentum $\propto n^{x}$
$∴ \frac{m c Z}{137 n} \times \frac{nh}{2 π} \propto n^{x}$
$n^{0} \propto n^{x}$
$\Rightarrow x = 0$