Bohr Model: Orbits, Speed & Angular Momentum

When an electron in hydrogen atom revolves in a stationary orbit, it

Which of the following is an integral multiple of $\frac{h}{2\pi}$ in Bohr's model of an hydrogen atom?

The angular momentum of the electron in the third Bohr orbit of a hydrogen atom is '$l$' so its angular momentum in the fourth Bohr orbit is

In the hydrogen atom, radii of the first four Bohr orbits are related as

In Bohr's theory of hydrogen atom, 'r' is the radius of the orbit, 'V' is the speed of electron and E is the total energy of the electron. Out of the following which physical quantity is inversely proportional to principal quantum number?

The de Broglie wavelength of an electron moving in the $n^{th}$ Bohr orbit of radius '$r$' is

The de-Broglie wavelength of an electron moving in the $n^{th}$ Bohr orbit of radius 'r' is

The de Broglie wavelength of the electron in the ground state is $\lambda_1$ and that in the $n = 3$ level is $\lambda_3$ then $\lambda_3$ is given by

When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, the de-Broglie wavelength associated with it

The magnetic moment of electron due to orbital motion is proportional to

($n$ = principal quantum number)

The orbital magnetic moment $(m_{orb})$ of a revolving electron around the nucleus varies with the principal quantum number ($n$) as

The force acting on the electron in hydrogen atom (Bohr's theory) is related to the principal quantum number n as

The angular momentum of an electron in Bohr's hydrogen atom having energy $(-0.544)$ eV is ($h$ = Planck's constant)

The energy of an electron in an orbit of the Bohr's atom is $-0.04E_0$ eV where $E_0$ is the ground state energy. If $L$ is the angular momentum of the electron in this orbit and $h$ is the Planck's constant, then

$\frac{2\pi L}{h}$ is ________:

If the difference between $(n+1)^{th}$ Bohr radius and $n^{th}$ Bohr radius is given by $(n-1)^{th}$ Bohr radius, then the value of n is

The triply ionized beryllium (Be$^{+++}$) has the same electron orbital radius as that of the ground state of hydrogen. Hence, the energy state of triply ionized beryllium is (Given $Z = 4$ for beryllium)

In the first excited state of hydrogen atom, the energy of its electron is -3.4 eV. The radial distance of the electron from the hydrogen nucleus in this case is approximately:

(Take $1\text{ eV} = 1.6 \times 10^{-19}\text{ J},\ e = 1.6 \times 10^{-19}\text{ C}$ and $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\text{ N m}^2/\text{C}^2$)

Two electrons are moving in orbits of two hydrogen like atoms with speeds $3 \times 10^{5}\text{ m/s}$ and $2.5 \times 10^{5}\text{ m/s}$ respectively. If the radii of these orbits are nearly same then the possible order of energy states are ______ respectively.

In hydrogenth atom, an electron jumps from higher orbit to lower orbit so that radius of the lower orbit is $\left(\frac{1}{4}\right)$ of radius of higher orbit. If speed of electron in higher orbit was V, then speed in lower orbit is

Consider that an electron is revolving in an excited state of Hydrogen atom with velocity $\sqrt{25.6} \times 10^{5}\text{ m s}^{-1}$. The radius of the orbit is $x \times 10^{-9}\text{ m}$. The value of $x$ is:

[Take the mass of electron to the $9 \times 10^{-31}\text{ kg}$, charge of electron $= -1.6 \times 10^{-19}\text{ C}$ and $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\text{ N m}^2\text{C}^{-2}$ ]

The moment of inertia of the electron moving in the second Bohr orbit of a hydrogen atom is [$m$ = mass of electron, $h$ = Planck's constant, $e$ = charge on electron, $\varepsilon_0$ = permittivity of free space]

Using Bohr's atomic model, the orbital period of electron in hydrogen atom in the $n$th orbit is ($\epsilon_0$=permittivity of free space, h=Planck's constant, m = mass of electron, e = electronic charge)

The number of revolutions per second made by an electron in the first Bohr orbit of hydrogen atom is ($h$ = Planck's constant, $m$ is the mass of electron and $r$ is the radius of the orbit.)

Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is ($\mu_0$ = permeability of free space, $\epsilon_0$ = permittivity of free space, $m$ = mass of electron, $e$ = electronic charge)

An electron is revolving in a circular orbit of radius 'r' in hydrogen atom. Using Bohr's theory, the angular momentum of the electron is

(M = magnetic dipole moment, m = mass of electron)

Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom ________.

The ratio of centripetal acceleration for an electron revolving in 3rd and 5th Bohr orbit of hydrogen atom is

Using Bohr's quantisation condition, what is the rotational kinetic energy in the second orbit for a diatomic molecule (I = moment of inertia of diatomic molecule, h = Planck's constant)

Bohr model is applied to a particle of mass $m$ and charge $q$ is moving in a plane under the influence of a transverse magnetic field $B$. The energy of the charged particle in $n^{th}$ level will be ($h$ = Planck's constant)

Bohr model is applied to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a transverse magnetic field B. The energy of the charged particle in the $n^{th}$ level will be (h=Planck's constant)

Given below are two statements:

Statement (I): The dimensions of Planck's constant and angular momentum are same. Statement (II): In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.

In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements: one is labelled as $\textbf{Assertion A}$ and the other is labelled as Reason $\textbf{R}$

Assertion A: The Bohr model is applicable to hydrogen and hydrogen-like atoms only. Reason $\textbf{R}$: The formulation of Bohr model does not include repulsive force between electrons. In the light of the above statements, choose the correct answer from the options given below

Considering the Bohr model of hydrogen like atoms, the ratio of the radius of $5$th orbit of the electron in $\text{Li}^{2+}$ and $\text{He}^{+}$is

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\text{Li}^{++}$ ion in its ground state is given by $\frac{1}{X}a_0$, where $X =$ __________ (Where $a_0$ is the first Bohr's radius.)

The frequency of revolution of an electron in the $n$th orbit of hydrogen atom is

The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as:

The magnetic moment of electron due to orbital motion is proportional to ( $n =$ principal quantum number)

In hydrogen atom in its ground state, the first Bohr orbit has radius ' $r_1$ '. When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is

The ratio of angular momentum of an electron in $n$th orbit of hydrogen atom to the velocity of electron in $n$th orbit is proportional to

Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is ( $h =$ Planck's constant, $I =$ moment of inertia of diatomic molecule)

A particle of mass $m$ is moving around the origin with a constant force $F$ pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the $n$th orbit and the particle's speed $v$ in the orbit depend on $n$ as

The angular momentum of the electron in the third Bohr orbit of hydrogen atom is ' $l$ '. Its angular momentum in the fourth Bohr orbit is

According to Bohr's theory, the moment of momentum of an electron revolving in $4$th orbit of hydrogen atom is:

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

The radius of innermost orbit of hydrogen atom is $5.3 \times 10^{-11}\text{ m}$. The radius of fourth allowed orbit of hydrogen atom is

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' $r_0$ ' is the radius of the ground state orbit, ' $m$ ' is the mass, ' e ' is the charge on the electron and ' $\varepsilon_0$ ' is the permittivity of vacuum, the speed of the electron is

In hydrogen atom, if $V_n$ and $V_p$ are orbital velocities in $n$th and $p$th orbit respectively, then the ratio $V_p : V_n$ is

When an electron orbiting in hydrogen atom in its ground state jumps to higher excited state, the de- Broglie wavelength associated with it

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is

The angular momentum of an electron in a hydrogen atom is proportional to: (Where $r$ is the radius of orbit of electron)

Radius of first orbit in H -atom is ' $a_0$ ' Then, de-Broglie wavelength of electron in the third orbit is

Using Bohr's model, the orbital period of electron in hydrogen atom in $n$th orbit is ( $m =$ mass of electron, $h =$ Planck's constant, $e =$ electronic charge, $\varepsilon_0 =$ permittivity of free space)

An electron revolving in $n$th Bohr orbit has magnetic moment $\mu_n$. If $\mu_n \propto n^x$, the value of $x$ is

Acceleration of an electron in the first Bohr's orbit is proportional to ($m =$ mass of electron, $r =$ radius of the orbit, $h =$ Planck's constant)

A diatomic molecule has moment of inertia ' I ', By applying Bohr's quantization condition, its rotational energy in the $n$th level is $[n \geq 1]$ [h= Planck's constant]

When an electron is excited from its 4 th orbit to 5 th stationary orbit, the change in the angular momentum of electron is approximately.

(Planck's constant $= h = 6.63 \times 10^{-34}\text{ J-s}$)

The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be

The radius of inner most orbit of hydrogen atom is $5.3 \times 10^{-11}\text{ m}$. What is the radius of third allowed orbit of hydrogen atom?

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

The radius of fifth orbit of the $\text{Li}^{++}$ is __________ $\times 10^{-12}\text{ m}$.

Take: radius of hydrogen atom $= 0.51\ \mathring{A}$

The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of hydrogen atom is

Speed of an electron in Bohr's $7$th orbit for Hydrogen atom is $3.6 \times 10^{6}\text{ m/s}$. The corresponding speed of the electron in $3$rd orbit, in $\text{m/s}$ is:

For an electron moving in the $n$th Bohr orbit the deBroglie wavelength of an electron is

Magnetic field at the centre of the hydrogen atom due to motion of electron in $n$th orbit is proportional to

The orbital magnetic moment associated with orbiting electron of charge '$e$' is

The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number '$n$' as

A light of energy $12.75\text{ eV}$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi} \times 10^{-17}\text{ eVs}$. The value of $x$ is ___________ (use $h = 4.14 \times 10^{-15}\text{ eVs},\ c = 3 \times 10^{8}\text{ ms}^{-1}$ ).

The radius of $2$nd orbit of $\text{He}^{+}$ of Bohr's model is $r_1$ and that of fourth orbit of $\text{Be}^{3+}$ is represented as $r_2$. Now the ratio $\frac{r_2}{r_1}$ is $x : 1$. The value of $x$ is ___________.

Experimentally it is found that $12.8\text{ eV}$ energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $\frac{9}{x} \times 10^{-10}\text{ m}$. The value of the $x$ is __________.

$\Bigg(1\text{ eV} = 1.6 \times 10^{-19}\text{ J},\ \frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ Nm}^2/\text{C}^2$ and electronic charge $= 1.6 \times 10^{-19}\text{ C}\Bigg)$

An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage change in the speed of electron?

If the radius of the first Bohr orbit is '$r$' then the de-Broglie wavelength of the electron in the $4$th orbit will be

Bohr model is applied to a particle of mass '$m$' and charge '$q$' moving in a plane under the influence of a transverse magnetic field '$B$'. The energy of the charged particle in the $n$th leve will be $[h =$ Planck's constant $]$

A small particle of mass $m$ moves in such a way that its potential energy $U = \frac{1}{2} m\omega^2 r^2$ where $\omega$ is constant and $r$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of $n$th orbit will be proportional to,

Given below are two statements:

Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E1) to higher energy orbit (E2), is given as hf = E1 $-$ E2

Statement II: The jumping of electron from higher energy orbit (E2) to lower energy orbit (E1) is associated with frequency of radiation given as f = (E2 $-$ E1)/h

This condition is Bohr's frequency condition.

In the light of the above statements, choose the correct answer from the options given below:

Let R1 be the radius of the second stationary orbit and R2 be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio $\frac{R_1}{R_2}$ is:

Using Boh'r model of quantization of angular momentum the relation between the radius 'r' of the $n$th allowed orbit of quantum number 'n' for an electron in hydrogen atom is:

The ratio for the speed of the electron in the 3rd orbit of He+ to the speed of the electron in the 3rd orbit of hydrogen atom will be:

The momentum of an electron revolving in $n$th orbit is given by:

(Symbols have their usual meanings)

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by:

A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by:

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of:

(Given, Planck's constant = 6.6 $\times$ 10$-$34 Js).

Using Bohr's model, the orbital period of electron in hydrogen atom in the $n$th orbit is $(\varepsilon_0 =$ permittivity of vacuum, $h =$ Planck's constant, $m =$ mass of electron, $e =$ electronic charge)

If an electron is moving in the nth orbit of the hydrogen atom, then its velocity (vn) for the nth orbit is given as: