In the hydrogen atom spectrum, let E_1 and E_ | vedclass

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

Question

(D) The energy of a photon emitted during a transition in a hydrogen atom is given by the Rydberg formula: $\Delta E = 13.6 \left( \frac{1}{n_f^2} - \

Vedclass · Accepted Answer

$\frac{5}{27}$

Vedclass · Answer

(D) The energy of a photon emitted during a transition in a hydrogen atom is given by the Rydberg formula: $\Delta E = 13.6 \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight) 	ext{ eV}$.For the transition $n=2 ightarrow n=1$, the energy $E_1$ is:$E_1 = 13.6 \left( \frac{1}{1^2} - \frac{1}{2^2} ight) = 13.6 \left( 1 - \frac{1}{4} ight) = 13.6 	imes \frac{3}{4} 	ext{ eV}$.For the transition $n=3 ightarrow n=2$, the energy $E_2$ is:$E_2 = 13.6 \left( \frac{1}{2^2} - \frac{1}{3^2} ight) = 13.6 \left( \frac{1}{4} - \frac{1}{9} ight) = 13.6 	imes \frac{5}{36} 	ext{ eV}$.Now, calculating the ratio $E_2 / E_1$:$\frac{E_2}{E_1} = \frac{13.6 	imes (5/36)}{13.6 	imes (3/4)} = \frac{5}{36} 	imes \frac{4}{3} = \frac{5}{9 	imes 3} = \frac{5}{27}$.

In the hydrogen atom spectrum, let $E_1$ and $E_2$ be the energies for the transitions $n=2 \rightarrow n=1$ and $n=3 \rightarrow n=2$ respectively. The ratio $E_2 / E_1$ is

Similar Questions

How much energy is needed to release the electron from the second excited state in the hydrogen atom (in $eV$)?

Energy of an electron (in $eV$) in the $2^{nd}$ orbit of a $He^{+}$ ion is (in $.6$)?

The ratio of energies of photons produced due to the transition of an electron in a hydrogen atom from its $(i)$ second to first energy level and (ii) highest energy level to second energy level is: (in $3:1$)

Inner shell electrons in atoms moving from one energy level to another lower energy level produce

When a hydrogen atom transitions from $n=2$ to $n=1$, it emits a photon. The recoil speed of the atom is $\frac{x}{5} \,m/s$. Find the value of $x$. (Use: mass of hydrogen atom $= 1.6 \times 10^{-27} \,kg$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module