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If the mass of electron is doubled, then find the new radius (in $\overset{\circ}{A}$ ) of $1^{st}$ orbit of $H$ -atom?

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Important Questions on Structure of Atoms and Nuclei

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

A hydrogen atom in ground state absorbs

10.2 e V

of energy. The orbital angular momentum of the electron is increased by

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Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

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}

)

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The time period of revolution of electron in its ground state orbit in a hydrogen atom is

1.6 \times 10^{- 16} s .

The frequency of revolution of the electron in its first excited state (in

s^{- 1}

) is:

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

To which of the following the angular velocity of the electron in the $n^{th}$ Bohr orbit is proportional?

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

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}}

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

In a hydrogen atom, an electron of mass

9.1 \times 10^{- 31} kg

revolves about a proton in circular orbit of radius

0.53 A .

The radial acceleration and angular velocity of electron are respectively

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

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:

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

What are the limitations of Bohr's theory of hydrogen atom?

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

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) $= 6 .6 \times 10^{- 34} J s$

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

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)

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

A particle

A

of mass

m

and charge

q

is accelerated by a potential difference of

50 V .

Another particle

B

of mass

4 m

and charge

q

is accelerated by a potential difference of

2500 V .

The ratio of de-Broglie wavelengths

\frac{λ_{A}}{λ_{B}}

is close to:

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

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,

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The mass of 0.6 atom of nitrogen is_____:

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The difference between the radii of

n^{th}

and

(n + 1)^{t h}

orbits of hydrogen atom is equal to the radius of

(n - 1)^{th}

orbit of hydrogen. The angular momentum of the electron in the

n^{th}

orbit is

______

(

h

is Planck's constant)

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The angular momentum of electron in Hydrogen atom is proportional to (

r

is the radius of the atom)

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

A particle of mass

m

moves in a circular orbit in a central potential field

U (r) = U_{0} r^{4} .

If Bohr's quantization conditions are applied, radii of possible orbitals

r_{n}

vary with

n^{\frac{1}{α}}

, where

α

is _______ .

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

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

n = 1

) is :

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

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,

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

Highly excited states for hydrogen like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n >> 1. Which of the following statement(s) is (are) true?

If the mass of electron is doubled, then find the new radius (in A∘) of 1st orbit of H-atom?

Important Questions on Structure of Atoms and Nuclei

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If the mass of electron is doubled, then find the new radius (in $\overset{\circ}{A}$ ) of $1^{st}$ orbit of $H$ -atom?