Question

Electrons are revolving around the nucleus in $n_1^{th}$orbit of an atom, have atomic number $z_1,$and in the $n_2^{th}$ orbit of other atom, have atomic number $Z_2,$then:
(Where P=Linear momentum, L=Angular momentum, f=frequency of revolution and K.E.=kinetic energy]

• A. $\frac{L_1}{L_2}=\frac{n_1}{n_2}$
• B. $\frac{P_1}{P_2}=\frac{Z_1{n}_2}{Z_2{n}_1}$
• C. $\frac{f_1}{f_2}={\left(\frac{Z_2}{Z_1}\right)}^2{\left(\frac{n_1}{n_2}\right)}^3$
• D. $\frac{{(K.E.)}^1}{(K.E.{)}^2}={(\frac{Z_1}{Z_2}.\frac{n_2}{n_1})}^2$

Answer 1

Answer: (A), (B), (D)

$\frac{L_1}{L_2}=\frac{n_1}{n_2}$
$\frac{P_1}{P_2}=\frac{Z_1{n}_2}{Z_2{n}_1}$
$\frac{{(K.E.)}^1}{(K.E.{)}^2}={(\frac{Z_1}{Z_2}.\frac{n_2}{n_1})}^2$

According to the Bohr model, angular momentum, $L=mvr=nh/2\pi$.

So, $\frac{L_1}{L_2}=\frac{n_1}{n_2}$ and $K.E=-\frac{13.6Z^2}{n^2}$

$⟹\frac{(K.E{)}_1}{(K.E.{)}_2}=(\frac{Z_1}{Z_2}.\frac{n_2}{n_1}{)}^2$

Also, as $P=\sqrt{2mK.E}$

$⟹\frac{P_1}{P_2}=\frac{Z_1}{Z_2}\times \frac{n_2}{n_1}$