An atomic emission spectrum of hydrogen shows three wavelengths: 1875 nm, 1282 nm, and 1093 nm.

An atomic emission spectrum of hydrogen shows three...

Key Concepts

Spectral Series

Spectral series are groups of related spectral lines that result from transitions ending at the same principal quantum number. For hydrogen, series such as the Lyman, Balmer, and Paschen are defined by final states of n=1, 2, and 3 respectively. In the given context, the wavelengths in the infrared region correspond to the Paschen series, where electrons transition to the n=3 energy level.

Rydberg Formula

The Rydberg formula relates the reciprocal wavelength of emitted or absorbed light to the difference between the inverse squares of the principal quantum numbers of the involved energy levels. This formula is essential for calculating and assigning the wavelengths to specific electronic transitions in hydrogen.

Atomic Emission Spectrum

An atomic emission spectrum is produced when electrons in an atom transition from higher to lower energy levels, emitting photons with energies specific to the differences between these levels. This spectrum is characteristic of the element, with each spectral line corresponding to a unique electronic transition.

Hydrogen Energy Levels and Quantum Transitions

Hydrogen atoms have discrete energy levels defined by quantum numbers. When an electron moves from a higher level to a lower one, it emits a photon with a wavelength determined by the energy difference between those levels. Understanding these transitions is fundamental for identifying which levels are involved based on the observed wavelengths.

Transcript

00:01 The complete explanation of the solution is that when there is a transition between two energy level, the transition energy is given by the expression given below, that is delta e equal to hv, or delta e equal to h, c divided by lambda.

00:23 Here, delta e is the transition energy.

00:27 H is the planks constant, c is the velocity of light, and we will.

00:31 The frequency and lambda is the wavelength of light so the values of h and c are 6 .626 multiplied by 10 to the power minus 34 j dot s and 3 multiplied by a 10 to the power 8 meter per second respectively the energy associated with a wavelength of 1875 and m is calculated using the expression of energy given above as follows the delta e is equal to 6 .26 multiplied by 10 to the power minus 34 j dot s multiplied by 3 multiplied by 10 to 8 meter per second divided by 1875 this will be equal to and by calculating this here we get the final value is 1 .06 multiply by 10 to the power minus 19 0 .0 6 multiplied by 10 to the power minus 19 so this value of energy change is the transition energy corresponding to a transition from the fourth energy level to the third energy level of the hydrogen atom.

01:53 Hence, the transition associated with the wavelength of 1875nm is n equal to 4 and equal to 3.

02:04 Now here the energy associated with a wavelength of 1282nm is calculated using the expression of energy given above as follows.

02:24 We again use the same expression to calculate and here we calculate the final value is 1 .55 multiplied by 10 to 19 jule.

02:34 So this value of energy change is the transition energy corresponding to a transition...

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