(a) Calculate the radius of the first three Bohr orbits for hydrogen. (Planck's constant h = 6 . 6262 × 10 - 34 Js ; Mass of electron m = 9 . 1091 × 10 - 31 kg : Charge on electron e = 1 . 60210 × 10 - 19 C ; Permittivity of vacuum ε 0 = 8 . 854185 × 10 - 12 kg - 1 m - 3 A 2 .) (b) Use these radius to calculate the velocity of an electron in each of these three orbits.

(a) Calculation of radius of Bohr orbit for hydrogen atom: r = n 2 h 2 4 π 2 mKZe 2 K = 1 4 π ∈ o = 9 × 10 9 Nm 2 C - 2 r = n 2 ( 6 . 6262 × 10 - 34 ) 2 4 ( 3 . 14 ) 2 ( 9 . 1091 × 10 - 31 ) ( 9 × 10 9 ) Z ( 1 . 60210 × 10 - 19 ) 2 r = 0 . 529 × 10 - 10 × n 2 Z m For Hydrogen atom, Z = 1 For first Bohr orbit, n = 1 r = 0 . 529 × 10 - 10 × 1 2 1 m r = 0 . 529 × 10 - 10 m For second Bohr orbit, n = 2 r = 0 . 529 × 10 - 10 × 2 2 1 m r = 2 . 116 × 10 - 10 m For third Bohr orbit, n = 3 r = 0 . 529 × 10 - 10 × 3 2 1 m r = 4 . 761 × 10 - 10 m (b) Calculation of velocity in an orbit: According to Bohr postulate, the magnitude of electrostatic force of attraction is balanced by centrifugal force. F e = F c - KZe 2 r 2 = mv 2 r KZe 2 r 2 = mv 2 r v = KZe 2 rm 1 2 = 9 × 10 9 Z ( 1 . 602 × 10 - 19 ) 2 r ( 9 . 1091 × 10 - 31 ) 1 2 = 252 . 93 × Z r 1 2 For first Bohr orbit, n = 1 v = 252 . 93 × 1 0 . 529 × 10 - 10 1 2 v = 2 . 19 × 10 6 m s - 1 . For second Bohr orbit, n = 2 v = 252 . 93 × 1 2 . 12 × 10 - 10 1 2 v = 1 . 09 × 10 6 m s - 1 . For third Bohr orbit, n = 3 v = 252 . 93 × 1 4 . 761 × 10 - 10 1 2 v = 0 . 729 × 10 6 m s - 1 .

Which of the following species does the Bohr's theory apply to? (a) H (b) H + (c) He (d) He + (e) Li (f) Li + (g) Li + 2 (h) Be (i) Be + (j) Be 2 + (k) Be 3 +

Bohr's theory is valid only for mono-electronic species and it is not valid for multi-electronic species. Species Electronic configuration Number of electrons Bohr's theory H 1 s 1 1 Applicable H + 1 s 0 0 Not applicable He 1 s 2 2 Not applicable He + 1 s 1 1 Applicable Li 1 s 2 2 s 1 3 Not applicable Li + 1 s 2 2 Not applicable Li + 2 1 s 1 1 Applicable Be 1 s 2 2 s 2 4 Not applicable Be + 1 s 2 2 s 1 3 Not applicable Be + 2 1 s 2 2 Not applicable Be + 3 1 s 1 1 Applicable

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Give the equation which explains the different series of lines in the atomic spectrum of hydrogen. Who is the equation named after? Explain the various terms involved.

Important Questions on Atomic Structure and the Periodic Table

HARD

JEE Advanced

IMPORTANT

Concise Inorganic Chemistry>Chapter 1 - Atomic Structure and the Periodic Table>Exercise 1>Q 4

(a) Calculate the radius of the first three Bohr orbits for hydrogen. (Planck's constant

h = 6.6262 \times 10^{- 34} Js;

Mass of electron

m = 9.1091 \times 10^{- 31} kg :

Charge on electron

e = 1.60210 \times 10^{- 19} C;

Permittivity of vacuum

ε_{0} = 8.854185 \times 10^{- 12} {kg}^{- 1} m^{- 3} A^{2}

.)
(b) Use these radius to calculate the velocity of an electron in each of these three orbits.

HARD

JEE Advanced

IMPORTANT

Concise Inorganic Chemistry>Chapter 1 - Atomic Structure and the Periodic Table>Exercise 1>Q 5

The Balmer series of spectral lines for hydrogen appear in the visible region. What is the lower energy level that these electronic transitions start from, and what transitions correspond to the spectral lines at

379.0 nm

and

430.0 nm

, respectively?

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JEE Advanced

IMPORTANT

Concise Inorganic Chemistry>Chapter 1 - Atomic Structure and the Periodic Table>Exercise 1>Q 6

What is the wave number and wave length of the first transition in the Lyman, Balmer and Paschen series in the atomic spectra of hydrogen?

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JEE Advanced

IMPORTANT

Concise Inorganic Chemistry>Chapter 1 - Atomic Structure and the Periodic Table>Exercise 1>Q 7

Which of the following species does the Bohr's theory apply to?

(a) $H$

(b) $H^{+}$

(d) ${He}^{+}$

(e) $Li$

(f) ${Li}^{+}$

(g) ${Li}^{+ 2}$

(h) $Be$

(i) ${Be}^{+}$

(j) ${Be}^{2 +}$

(k) ${Be}^{3 +}$

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Concise Inorganic Chemistry>Chapter 1 - Atomic Structure and the Periodic Table>Exercise 1>Q 8

How is the Bohr theory of the hydrogen atom different from that of Schrödinger?

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JEE Advanced

IMPORTANT

Concise Inorganic Chemistry>Chapter 1 - Atomic Structure and the Periodic Table>Exercise 1>Q 11

Explain (a) the Pauli exclusion principle and (b) Hund's rule. Show how these are used to specify the electronic arrangements of the first

20

elements in the periodic table.

MEDIUM

JEE Advanced

IMPORTANT

Concise Inorganic Chemistry>Chapter 1 - Atomic Structure and the Periodic Table>Exercise 1>Q 12

What is an orbital? Draw the shapes of the

2 s, 2 p_{x}, 2 p_{y}, 2 p_{z}, 3 d_{xy}

and

3 d_{z^{2}}

orbitals.

EASY

JEE Advanced

IMPORTANT

Concise Inorganic Chemistry>Chapter 1 - Atomic Structure and the Periodic Table>Exercise 1>Q 13

Give the names and symbols of the four quantum numbers required to define the energy of electrons in atoms. What do these quantum numbers relate to, and what numerical values are possible for each? Show how the shape of the periodic table is related to these quantum numbers.

Give the equation which explains the different series of lines in the atomic spectrum of hydrogen. Who is the equation named after? Explain the various terms involved.

Important Questions on Atomic Structure and the Periodic Table

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