(a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.

Solution

(a) From the relation,

$v = \frac{c}{n} α, where α = \frac{2 π {Ke}^{2}}{ch} = 0.0073$

Therefore, the speed of electron in hydrogen atom in n=1, 2 and 3 is given by,
   $v_{1} = \frac{3 \times 10^{8}}{1} \times 0.0073 = 2.19 \times 10^{6} m / s v_{2} = \frac{3 \times 10^{8}}{2} \times 0.0073 = 1.095 \times 10^{6} m / s v_{3} = \frac{3 \times 10^{8}}{3} \times 0.0073 = 7.3 \times 10^{5} m / s .$

(b) Orbital period in each of the level is given by,

$T = \frac{2 πr}{v} As r_{1} = 0.53 \times 10^{- 10} m$

$T_{1} = \frac{2 π \times 0.53 \times 10^{- 10}}{2.19 \times 10^{6}} = 1.52 \times 10^{- 16} s$ '

As, $r_{2} = 4 r_{1} and v_{2} = \frac{1}{2} v_{1}$

$∴$     $T_{2} = 8 T_{1} = 8 \times 1.52 \times 10^{- 16} s = 1.216 \times 10^{- 15} s$

Also as, $r_{3} = 9 r_{1} and v_{3} = \frac{1}{3} v_{1}$
$∴$ $T_{3} = 27 T_{1} = 27 \times 1.52 \times 10^{- 16} s = 4.1 \times 10^{- 15} s .$

T₁, T₂ and T₃ are respectively the orbital time period for n₁, n₂and n₃ .

Some More Questions From Wave Optics Chapter

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

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Wave Optics

(a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.

Some More Questions From Wave Optics Chapter

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Wave Optics

(a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.

Some More Questions From Wave Optics Chapter

In the ground state of __________ electrons are in stable equilibrium, while in __________ electrons always experience a net force. (Thomson's model/Rutherford's model).

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a _____________ but has a highly non-uniform mass distribution in __________ (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)