A particular hydrogen-like ion emits radiatio | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The frequency of emitted radiation is given by $
u = R c Z^2 \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight)$.For the transition $n=2$ to $n=1$:

Vedclass · Accepted Answer

$32$

Vedclass · Answer

(A) The frequency of emitted radiation is given by $
u = R c Z^2 \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight)$.For the transition $n=2$ to $n=1$:$
u_1 = K \left( \frac{1}{1^2} - \frac{1}{2^2} ight) = K \left( 1 - \frac{1}{4} ight) = K \left( \frac{3}{4} ight) = 3 	imes 10^{15} \,Hz$.For the transition $n=3$ to $n=1$:$
u_2 = K \left( \frac{1}{1^2} - \frac{1}{3^2} ight) = K \left( 1 - \frac{1}{9} ight) = K \left( \frac{8}{9} ight)$.Taking the ratio:$\frac{
u_2}{
u_1} = \frac{K(8/9)}{K(3/4)} = \frac{8}{9} 	imes \frac{4}{3} = \frac{32}{27}$.Therefore, $
u_2 = \frac{32}{27} 	imes 3 	imes 10^{15} \,Hz = \frac{32}{9} 	imes 10^{15} \,Hz$.Comparing this with $\frac{x}{9} 	imes 10^{15} \,Hz$, we get $X = 32$.

$A$ particular hydrogen-like ion emits radiation of frequency $3 \times 10^{15} \,Hz$ when it makes a transition from $n=2$ to $n=1$. The frequency of radiation emitted in a transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15} \,Hz$, where $X = \text{ . . . . . . }$.

Similar Questions

The radius of a hydrogen atom in the ground state is $0.53 \ Å$. After collision with an electron,it is found to have a radius of $2.12 \ Å$. The principal quantum number $n$ of the final state of the atom is:

In the Bohr model of the hydrogen atom,the linear momentum of the electron depends on the principal quantum number $n$ as:

The time period of revolution of an electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16} \; s$. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is:

In the Bohr model of the hydrogen atom,the force on the electron is proportional to which power of the principal quantum number $n$?

The orbital frequency of an electron in the hydrogen atom is proportional to

Vedclass Test Series

Exam Paper Generator

Online Exam Module