The radius of the orbit of an electron in a hydrogen atom is 5 . 3 × 10 - 11 m . Calculate its potential energy in eV . (charge of an electron e = 1 . 6 × 10 - 19 C , 1 4 π ε o = 9 × 10 9 Nm 2 C 2 )

We know that potential energy of an electron in orbit of the hydrogen atom (Using Rutherford model): U = - e 2 4 π ε o r where r is the radius of orbit. Given: Charge of the electron e = 1 . 6 × 10 - 19 C Radius of orbit r = 5 . 3 × 10 - 11 m 1 4 π ε o = 9 × 10 9 Nm 2 / C 2 Hence, potential energy: U = - 9 × 10 9 × 1 . 6 × 10 - 19 2 5 . 3 × 10 - 11 = - 4 . 35 × 10 - 18 J = - 4 . 35 × 10 - 18 1 . 6 × 10 - 19 eV = - 27 . 2 eV

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.

A difference of 2 . 3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

The Separation of two energy levels in an atom, E = 2 . 3 eV = 2 . 3 × 1 . 6 × 10 - 19 = 3 . 68 × 10 - 19 J The relation between energy and frequency is given by, E = h v Where, Planck’s constant h = 6 . 62 × 10 - 34 Js , and, ν is the frequency of radiation. ∴ ν = E ⁄ h = 3 . 68 × 10 - 19 6 . 62 × 10 - 34 = 5 . 55 × 10 14 Hz The radiation frequency is 5 . 6 × 10 14 Hz . Here, the symbols have their usual meaning.

E M B I B E

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 9

EASY

12th Karnataka Board

IMPORTANT

Earn 100

Evaluate the Rydberg's constant by putting the values of the fundamental constants in its expression.

Important Questions on Atoms

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 10

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

R = 1.097 \times 10^{7} m^{- 1}

and

c = 3 \times 10^{8} {ms}^{- 1}

.

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 11

Find the value of Rydberg's constant if the energy of electron in second orbit in hydrogen atom is

- 3.4 eV

.

EASY

12th Karnataka Board

IMPORTANT

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

The radius of the orbit of an electron in a hydrogen atom is

5.3 \times 10^{- 11} m

. Calculate its potential energy in

eV

. (charge of an electron

e = 1.6 \times 10^{- 19} C

,

\frac{1}{4 π ε_{o}} = 9 \times 10^{9} {Nm}^{2} C^{2}

)

MEDIUM

12th Karnataka Board

IMPORTANT

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

Give the results of Rutherford alpha scattering experiment.

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 14

How is impact parameter related to angle of scattering?

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 15

What is impact parameter and angle of scattering? How are they related to each other?

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 16

An electron in the ground state of hydrogen atom is revolving in anti-clockwise direction in circular orbit of Radius R, Fig. 20.20.

Question Image

The atom is placed in a uniform magnetic induction B such that the plane normal to the electron-orbit makes an angle of $30 °$ with the magnetic induction. Find the torque experienced by the orbital electron

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Atoms>Exercise>Q 17

Explain Rutherford's scattering of