Use Moseley's law to determine the atomic number of the target material. Characteristic X-rays of frequency 4 . 2 × 10 18 Hz are produced when the transition from L -shell to K -shell takes place in a certain target material. Given: Rydberg's constant R = 1 . 1 × 10 7 m - 1

Given, X-ray of frequency = 4 . 2 × 10 18 Hz Rydberg's Constant R = 1 . 1 × 10 7 m - 1 Use the Mosley's Law to determine the atomic number of the largest material. Transition if from L-shell ot K-shell, 1 λ = R Z - 1 2 1 n 1 2 - 1 n 2 2 or f c = R Z - 1 2 1 n 1 2 - 1 n 2 2 or 4 . 2 × 10 8 3 × 10 8 = 1 . 1 × 10 7 Z - 1 2 1 1 2 - 1 2 2 or 4 . 2 × 10 8 3 × 10 8 = 1 . 1 × 10 7 Z - 1 2 1 - 1 4 4 . 2 × 10 8 = 1 . 1 × 10 7 × 3 × 10 8 Z - 1 2 1 - 1 4 Z - 1 2 = 1697 Z - 1 ≃ 41 Z = 42 Hence, it is the required answer.

Explain the different types of spectral series.

When an electron in an excited state falls back to a lower energy state, it emits photon of particular energy which is equal to the difference in energies of two states. Rydberg formula gives a relation between energy difference between various energy levels and the wavelength of the photons. ν = R Z 2 1 n 1 2 - 1 n 2 2 where R is the Rydberg constant, Z is the atomic number and n 1 and n 2 are the principal quantum numbers of the orbit. The spectral lines are formed as a result of electronic transition from one energy level to another. For a hydrogen atom, these lines are divided into five series: (i) Lyman series: Lyman series is obtained when an electron jumps to the first orbit from any other outer orbit. The wavelengths of Lyman series lies in the ultraviolet region of the spectrum. (ii) Balmer series: Balmer series is obtained when an electron jumps to the second orbit from any other outer orbit. The wavelengths of Balmer series lies in the visible region of the spectrum. (iii) Paschen series: Paschen series is obtained when an electron jumps to the third orbit from any other outer orbit. The wavelengths of Paschen series lies in the infrared region of the spectrum. (iv) Brackett series: Brackett series is obtained when an electron jumps to the fourth orbit from any other outer orbit. The wavelengths of Brackett series lies in the infrared region of the spectrum. (v) Pfund series: This series is obtained when an electron jumps to the fifth orbit from any other outer orbit. The wavelengths of Pfund series lies in the infrared region of the spectrum.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 31

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The shortest wavelength present in the Brackett series of a spectral line is

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Important Questions on Atoms

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 1

State Bohr’s postulate to define stable orbits in hydrogen atom. How does de Broglie’s hypothesis explain the stability of these orbits ?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 2

Using the Rydberg formula, calculate the wavelength of the first four spectral lines in the Balmer series of the hydrogen spectrum.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 3

A particle of charge equal to that of an electron $- e$ and mass $208$ times the mass of an electron (called mu -meson) moves in a circular orbit around a nucleus of charge $+ 3 e$ (Take the mass of nucleus to be infinite). Assuming that the Bohr model is applicable to this system, Find the wavelength of the radiation emitted when the mu-meson jumps from the third orbit to the first orbit.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 4

What is the shortest wavelength present in the Paschen series of spectral lines?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 5

Use Moseley's law to determine the atomic number of the target material. Characteristic X-rays of frequency