The wavelength of the first member of Balmer series is 6563 Å . Calculate the wavelength of second member of Lyman series.

According to Rydberg formula, 1 λ = R 1 n 1 2 - 1 n 2 2 where R is the Rydberg constant. For the first member of Balmer series, n 1 = 2 , n 2 = 3 ∴ 1 λ = R 1 2 2 - 1 3 2 1 λ = 5 R 36 R = 36 5 λ - - - ( i ) For the second member of Lyman series, n 1 = 1 , n 2 = 3 ∴ 1 λ ' = R 1 1 2 - 1 3 2 λ ' = 9 8 R Putting the value of R from ( i ) , we get, λ ' = 9 8 5 λ 36 λ ' = 5 32 λ Given: λ = 6563 Å λ ' = 5 32 6563 ⇒ 1025 . 5 Å

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.

What are the limitations of Bohr's theory of hydrogen atom?

Limitations of Bohr's theory: (i) Bohr's theory is limited to simple atoms like hydrogen for which Z = 1 . It fails for atoms of elements for which Z > 1 . (ii) It failed to explain the Zeeman effect i.e when the spectral line gets split into various components in the presence of magnetic field. (iii) It failed to explain the Stark effect i.e when the spectral line gets split into almost negligible lines in the presence of electric field. (iv) It violates Heisenberg uncertainty principle.

E M B I B E

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 8

MEDIUM

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IMPORTANT

Earn 100

Define impact parameter.

Important Questions on Atoms

HARD

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 9

What is the difference between

α -

particle and helium atom?

HARD

12th Telangana Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 10

Explain the distance of closest approach and impact parameter.

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12th Telangana Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 11

Describe Rutherford atom model. What are the draw backs of this model?

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 12

Why does the mass of the nucleus not have any significance in scattering in Rutherford's experiment?

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 13

Describe Geiger-Marsden experiment on scattering of

α -

particles. How is the size of the nucleus estimated in this experiment?

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 14

Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 15

Calculate the highest frequency in Balmer series, using Balmer formula. Take