Which of the following electronic transitions | vedclass

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

Question

(C) The wavelength $(\lambda)$ of an emitted photon is inversely proportional to the energy difference $(\Delta E)$ between the two energy levels,give

Vedclass · Accepted Answer

$n = 4 \rightarrow n = 1$

Vedclass · Answer

(C) The wavelength $(\lambda)$ of an emitted photon is inversely proportional to the energy difference $(\Delta E)$ between the two energy levels,given by the relation $\Delta E = \frac{hc}{\lambda}$.To obtain the shortest wavelength,the energy difference $(\Delta E)$ must be the maximum.The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $E_n = -13.6 \ 	ext{eV} / n^2$.The energy difference for a transition from $n_2$ to $n_1$ is $\Delta E = 13.6 \ 	ext{eV} 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2})$.Comparing the given transitions:$(A)$ $n = 2 ightarrow n = 1$: $\Delta E \propto (1 - 0.25) = 0.75$$(B)$ $n = 3 ightarrow n = 1$: $\Delta E \propto (1 - 0.111) = 0.889$$(C)$ $n = 4 ightarrow n = 1$: $\Delta E \propto (1 - 0.0625) = 0.9375$$(D)$ $n = 4 ightarrow n = 3$: $\Delta E \propto (0.111 - 0.0625) = 0.0485$The transition $n = 4 ightarrow n = 1$ has the largest energy difference,and therefore,it corresponds to the shortest wavelength.

Which of the following electronic transitions in a hydrogen atom results in the emission of a spectral line with the shortest wavelength?

Similar Questions

Find the radius of the fourth orbit of a hydrogen atom if its radius of the first orbit is $R \text{ pm}$.

Time taken for an electron to complete one revolution in the Bohr orbit of hydrogen atom is

The first quantum mechanical model of the atom was proposed by ........

If the first emission in the Lyman series of a hydrogen atom occurs at $121.5 \ nm$,what will be the energy difference between the first and second orbits in $kJ/mol$?

If the $I.E.$ of $He^{+}$ is $54.4 \ eV$,then -

Vedclass Test Series

Exam Paper Generator

Online Exam Module