A line in lyman series of hydrogen atom has a wavelength of 1 . 03 × 10 - 7 m . What is the initial energy level of the electron?

A line in lyman series of hydrogen atom has a wavelength, λ = 1 . 03 × 10 - 7 m . Lyman series, n 1 = 1 , n 2 = ? We know, 1 λ = R H 1 n 1 2 - 1 n 2 2 Rydberg's constant, R H = 1 . 09678 × 10 7 m - 1 . Substitute the values in the above formula, 1 1 . 03 × 10 - 7 = 1 . 09678 × 10 7 1 1 2 - 1 n 2 2 ⇒ n 2 = 3 . So, the electron belongs to third energy level ( M = 3 ) originally.

The radius of the first electron orbit of a hydrogen atom is 5 . 3 × 10 - 11 m . What is the radius of the second orbit?

According to Bohr's theory, The radius of n t h orbit of a hydrogen atom is given by, r n = k n 2 where k = h 2 4 π 2 m K e 2 ≈ 5 . 3 × 10 - 11 m ∴ r n = 5 . 3 × 10 - 11 n 2 For n = 1 , we get, r 1 = 5 . 3 × 10 - 11 × 1 2 ∴ r 1 = 5 . 3 × 10 - 11 m Putting n = 2 , we get, r 2 = 5 . 3 × 10 - 11 × 4 r 2 = 21 . 2 × 10 - 11 m

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.

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

In 1911 , Rutherford conducted an experiment in which he bombarded alpha particles on a thin gold foil. In that experiment, he observed that: (i) Most of the alpha particles passed straight through the gold foil. (ii) Very few particles scattered by more than 1 ° . (iii) About 1 in 8000 particles deflected by more than 90 ° . Based on these observations, he came up with a new model of atom. According to his model of the atom: (i) Most of the atom was empty space with its entire positive charge concentrated in a very small space inside the atom. This space was called the nucleus. (ii) The size of the nucleus is very small as compared to the size of the atom. (iii) The nucleus is surrounded by negatively charged particles called electrons. The negative charge of electrons is equal to the positive charge of the nucleus. Therefore, an atom is electrically neutral. (iv) Electrons revolve around the nucleus in circular orbits. Drawbacks of Rutherford's model of atom: (i) According to Rutherford's model of atom, electrons revolve around the nucleus in a circular path and are constantly under centripetal force. As a result, the electrons must undergo acceleration. Charged particles undergoing acceleration radiates energy, thus, electrons loses energy continuously and eventually falls into the nucleus. Thus, it failed to explain the stability of the atom. (ii) According to Rutherford's model, the atoms should emit continuous spectrum instead of line spectrum. Thus, it failed to explain the existence of spectral lines in the hydrogen spectrum.

E M B I B E

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 29

HARD

12th Telangana Board

IMPORTANT

Earn 100

What do you understand by the phrase 'ground state atom'?

Important Questions on Atoms

HARD

12th Telangana Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 30

Derive an expression for potential and kinetic energy of an electron in any orbit of a hydrogen atom according to Bohr's atomic model. How does P.E change with increasing n?

HARD

12th Telangana Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 31

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

HARD

12th Telangana Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 32

Distinguish between excitation potential and ionization potential.

EASY

12th Telangana Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 33

A line in lyman series of hydrogen atom has a wavelength of

1.03 \times 10^{- 7} m .

What is the initial energy level of the electron?

HARD

12th Telangana Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 35

State the basic postulates of Bohr's theory of atomic spectra. Hence obtain an expression for the radius of orbit and the energy of orbital electron in a hydrogen atom.

HARD

12th Telangana Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Atoms>Exercise>Q 36

The radius of the first electron orbit of a hydrogen atom is