The radius of the innermost electron orbit of a hydrogen atom is 5 . 3 × 10 - 11 m . What are the radii of the n = 2 and n = 3 orbits?

The innermost orbit’s radius of a hydrogen atom, r 1 = 5 . 3 × 10 - 11 m Let r 2 be the radius of the orbit at n = 2 It is related to the radius of the innermost orbit as: r 2 = ( n ) 2 r 1 = 4 × 5 . 3 × 10 - 11 = 2 . 12 × 10 - 10 m For n = 3 , the respective orbit radius can be written as: r 3 = ( n ) 2 r 1 = 9 × 5 . 3 × 10 - 11 = 4 . 77 × 10 - 10 m The electronic orbit radius for ( n = 2 ) is 2 . 12 × 10 - 10 m and for ( n = 3 ) is 4 . 77 × 10 - 10 m Here, the symbols have their usual meaning.

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 35

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What is the angular momentum of an electron in the third orbit of an atom?

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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 36

According to the classical electromagnetic theory velocity of electron moving around a proton in hydrogen atom in an orbit of radius

5.3 \times 10^{- 11} m

is

2.2 \times 10^{6} m / s

. Calculate the initial frequency of the light emitted by the electron revolving around a proton in hydrogen atom.

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 12 - ATOMS>Exercise>Q 37

As per Bohr model, the minimum energy (in

eV

) required to remove an electron from the ground state of doubly ionized

Li

atom

(Z = 3)

is

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 12 - ATOMS>Exercise>Q 38

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

5.3 \times 10^{- 11} m

. What are the radii of the

n = 2

and

n = 3

orbits?

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 12 - ATOMS>Exercise>Q 39

The total energy of an electron in the first excited state of the hydrogen atom is about $- 3.4 eV$ .

(a)What is the kinetic energy of the electron in this state?

(b) What is the potential energy of the electron in this state?

(c) Which of the answers above would change if the choice of the zero of potential energy is changed?

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 12 - ATOMS>Exercise>Q 40

In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius $1.5 \times 10^{11} m$ with orbital speed $3 \times 10^{4} m ⁄ s$ . (Mass of earth $6 \times 10^{24} Kg$ .)