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The Bohr model of atoms

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Important Questions on Atomic Physics

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

An electron with kinetic energy

E

collides with a hydrogen atom in the ground state. The collision will be elastic

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

Consider third orbit of ${He}^{+}$ (helium), using non-relativistic approach, the speed of electron in this orbit will be given constant $K {=9×10}^{9}$ , $Z =2$ and $h$ (Planck's Constant) $= 6 .6 \times 10^{- 34} J s$

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths

λ_{N}, λ_{A}

respectively. The ratio

\frac{λ_{N}}{λ_{A}}

is closest to:

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

The acceleration of an electron in the first orbit of the hydrogen atom (

n = 1

) is :

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

In a hydrogen like atom electron makes transition from an energy level with quantum number

n

to another with quantum number

(n - 1)

. If

n >> 1

, the frequency of radiation emitted is proportional to :

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

According to Bohr's theory, the time averaged magnetic field at the centre (i.e., nucleus) of a hydrogen atom due to the motion of electrons in the

n^{t h}

orbit is proportional to: (

n =

principal quantum number)

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

If an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength

λ

. When it jumps from the fourth orbit to the third orbit, the corresponding wavelength of the photon will be

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

The total energy of an electron in an atom in an orbit is

- 3.4 e V .

Its kinetic and potential energies are, respectively,

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

A particle of mass,

m

moves around the origin in a potential,

\frac{1}{2} m ω^{2} r^{2}

, where

r

is the distance from the origin. Applying the Bohr model in this case, the radius of the particle in its

n^{th}

orbit in terms of

a = \sqrt{\frac{h}{(2 π m ω)}}

is,

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

The magnitude of acceleration of the electron in the $n^{th}$ orbit of hydrogen atom is $a_{H}$ and that of singly ionised helium atom is $a_{He}$ . The ratio $a_{H} : a_{He}$ is,

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

The wavelength of the first Balmer line caused by a transition from the

n = 3

level to the

n = 2

level in hydrogen is

λ_{1} .

The wavelength of the line caused by an electronic transition from

n = 5

n = 3

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

A particle of mass

m

moves in a circular orbit in a central potential field

U (r) = \frac{1}{2} k r^{2} .

If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number

n

as:

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

A donor atom in a semiconductor has a loosely bound electron. The orbit of this electron is considerably affected by the semiconductor material but behaves in many ways like an electron orbiting a hydrogen nucleus. Given that the electron has an effective mass of

0.07 m_{e}

, where

m_{e}

is mass of the free electron and the space in which it moves has a permittivity

13 ε_{0},

then the radius of the electron's lowermost energy orbit will be close to (take, the Bohr radius of the hydrogen atom is

0.53 \overset{°}{A}

)

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

An electron in a hydrogen atom jumps from second Bohr orbit to ground state and the energy difference of the two states is radiated in the form of photons. These are then allowed to fall on a metal surface having a work-function equal to

4.2 eV

, then the stopping potential is [Energy of electron in

n^{th}

orbit

= - \frac{13 .6}{n^{2}} eV

]

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

An electron in a hydrogen atom makes a transition from

n = 2

n = 1

and emits a photon. This photon strikes a doubly ionized lithium atom which was already in an excited state and completely removes the orbiting electron. The least quantum number for the excited state of the lithium-ion for the process is

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths

\frac{λ_{1}}{λ_{2}}

of the photons emitted in this process is:

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius

4.65 Å

). The de-Broglie wavelength of this electron is:

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

To calculate the size of a hydrogen anion using the Bohr model, we assume that its two electrons move in an orbit such that they are always on diametrically opposite sides of the nucleus. With each electron having the angular momentum,

♄ = \frac{h}{2 π},

and taking electron interaction into account the radius of the orbit in terms of the Bohr radius of a hydrogen atom

a_{B} = \frac{4 π ε_{0} h^{2}}{m e^{2}}

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

In a Frank - Hertz experiment, an electron of energy

5 .6 eV

passes through mercury vapour and emerges with an energy

0 .7 eV .

The minimum wavelength of photons emitted by mercury atoms is close to:

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Physics>Modern Physics>Atomic Physics>Bohr’s Model of Hydrogen Atom

As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion

The Bohr model of atoms

Important Questions on Atomic Physics

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