Which of the following statements is true for hydrogen atom ?

Question

Which of the following statements is true for hydrogen atom ? (A) Angular moment propto (1/n) (B) Linear moment propto (1/n) (C) Radius propto (1/n) (D) Energy propto (1/n)

Tardigrade Admin · Accepted Answer

Angular momentum L = mvr = (nh/2π) or mv = (nh/2π r) Now, r propto n2 ∴ mv = p propto (nh/2π × n2) ⇒ p propto (h/2π n) or p propto (1/n) Energy, E propto (1/n2)

Q. Which of the following statements is true for hydrogen atom ?

Angular moment $\propto \frac{1}{n}$

Linear moment $\propto \frac{1}{n}$

Radius $\propto \frac{1}{n}$

Energy $\propto \frac{1}{n}$

Angular momentum
$L = m v r = \frac{nh}{2 π}$
or $m v = \frac{nh}{2 π r}$
Now, $r \propto n^{2}$
$∴ m v = p \propto \frac{nh}{2 π \times n ^{2}}$
$\Rightarrow p \propto \frac{h}{2 πn}$ or
$p \propto \frac{1}{n}$
Energy, $E \propto \frac{1}{n ^{2}}$

Q. Which of the following statements is true for hydrogen atom ?

Angular moment ∝n1​

Linear moment ∝n1​

Radius ∝n1​

Energy ∝n1​

Angular momentum L=mvr=2πnh​ or mv=2πrnh​ Now, r∝n2 ∴mv=p∝2π×n2nh​ ⇒p∝2πnh​ or p∝n1​ Energy, E∝n21​

Angular moment $\propto \frac{1}{n}$

Linear moment $\propto \frac{1}{n}$

Radius $\propto \frac{1}{n}$

Energy $\propto \frac{1}{n}$

Angular momentum
$L = m v r = \frac{nh}{2 π}$
or $m v = \frac{nh}{2 π r}$
Now, $r \propto n^{2}$
$∴ m v = p \propto \frac{nh}{2 π \times n ^{2}}$
$\Rightarrow p \propto \frac{h}{2 πn}$ or
$p \propto \frac{1}{n}$
Energy, $E \propto \frac{1}{n ^{2}}$