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Radius, velocity and the energy of nth Bohr orbital - (Concept)
According to Bohr’s theory for hydrogen atom:
(1) The stationary states for electron are numbered n = 1,2,3.......... These integral numbers are known as Principal quantum numbers.
(2) Bohr radius of nth orbit:
$\mathrm{r}_{\mathrm{n}}=0.529 \frac{\mathrm{n}^2}{\mathrm{Z}} \mathrm{A}^0$
where Z is atomic number and radius is calculated by the formula in angstrom (A0) (1A0=10-10 m)
(3) Velocity of electron in nth orbit:
$\mathrm{V}_{\mathrm{n}}=\left(2.18 \times 10^6\right) \frac{\mathrm{Z}}{\mathrm{n}} \mathrm{m} / \mathrm{s}$
where Z is atomic number
(4) Total energy of electron in nth orbit:
$E_n=-13.6 \frac{Z^2}{n^2} \mathrm{eV}=-2.18 \times 10^{-18} \frac{Z^2}{n^2} \mathrm{~J}$
where Z is atomic number
Depending upon the units given in the question, the respective formula can be used
(5) Time Period and Frequency of Revolution
Although the precise equations for time period and frequency of revolution are not required but still it is a good idea to look at the variations of these with the atomic number (Z) and the orbit number (n).
We know that Time period (T) is the time required for one complete revolution and that Frequency ($\nu$) is inverse of the time period
$\therefore T=\frac{\text { distance }}{\text { time }}=\frac{2 \pi r}{v}$
$\because r \propto \frac{\mathrm{n}^2}{\mathrm{Z}}$ and $v \propto \frac{\mathrm{Z}}{\mathrm{n}}$
$\therefore T \propto\left(\frac{n^2}{Z} \times \frac{n}{Z}\right) \propto\left(\frac{n^3}{Z^2}\right)$
$\therefore \nu=\left(\frac{1}{T}\right) \propto\left(\frac{Z^2}{n^3}\right)$
It is important that you remember all the above formula and relations
| Exam | Chapter |
| JEE MAIN | Atomic Structure |
Energy of an electron is given by ,Wavelength of light required to excite an electron in a hydrogen atom from level n = 1 to n = 2 will be:
(h=6.6210-34Js and c = 3.0
108 ms-1)
| A. |
|
| B. |
|
| C. |
|
| D. |
|
What is the work function (in eV) of the metal if the light of wavelength generates photoelectrons of velocity
from it ?
(Mass of electron =
Velocity of light =
Planck's constant =
Charge of electron = )
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The ground state energy of hydrogen atom is -13.6 eV. The energy of second excited state of ion in eV is:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Which one of the following about an electron occupying the 1s orbitals in a hydrogen atom is incorrect ? ( The Bohr radius is represented by )
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The radius of the second Bohr orbit, in terms of the Bohr radius, in
is :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
According to Bohr's atomic theory :
(A) Kinetic energy of electron is $\alpha \frac{Z^2}{n^2}$
(B) The product of velocity (v) of electron and principal quantum number (n), 'vn' $\alpha Z^2$
(C) Frequency of revolution of the electron in an orbit is $\alpha \frac{Z^3}{n^3}$.
(D) Coulombic force of attraction on the electron is $\alpha \frac{Z^3}{n^4}$.
Choose the most appropriate answer from the options given below :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
When an electron drops from a higher energy level to a low energy level then
| A. |
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| B. |
|
| C. |
|
| D. |
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The ratio of area covered by second orbit to the first orbit is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The energy of an electron in the first Bohr orbit of atom is
. The possible energy value of the excited state for an electron in Bohr orbits to hydrogen is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The Bohr orbit radius for the hydrogen atom(n=1) is approximately . The radius for the first excited state (n=2) orbit is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Which of the following electron transition in a hydrogen atom will require the largest amount of energy
| A. |
|
| B. |
|
| C. |
|
| D. |
|
As electron moves away from the nucleus, its potential energy
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The difference between the radii of 3rd and 4th orbits of is
The difference between the radii of 3rd and 4th orbits of
is
Ratio
is :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to . The value of
is_________. (
is the radius of Bohr's orbit) (Nearest integer)
[Given: ]
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If the radius of the Bohr's orbit of hydrogen atom is
and the radius of
Bohr's orbit is
. Then :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If the wavelength for an electron emitted from -atom is
, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is________ times. (Nearest integer)
[Given : ]
Mass of electron
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Given below are two statements:
Statement I : According to Bohr's model of an atom,qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.
Statement II : According to Bohr's model of an atom,qualitatively the magnitude of velocity of electron increases with decrease in principal quantum number.
In the light of the above statements,choose the most appropriate answer from the options given below:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If m and e are the mass and charge of the revolving electron in the orbit of radius r for hydrogen atom, the total energy of the
revolving electron will be :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The velocity of an electron in Bohr’s 3rd orbit of hydrogen is x. Then velocity in Bohr’s first orbit of Li2+ is:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
In a hydrogen atom, if energy of an electron in ground state is then that in the 2nd excited state is:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Number of waves in a Bohr’s orbit of H atom is 2. Its potential energy would be
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The radius (in Å) of the second Bohr orbit for the hydrogen atom is :
(Planck’s Const. h=6.6262×10−34 Js;
mass of electron=9.1091×10−31 kg;
charge of electron e=1.60210×10−19 C;
permittivity of vacuum =8.854185×10−12 kg−1m−3A2)
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The energy of an electron (in eV) in the first Bohr orbit of the H- atom is -13.6 eV. The energy value of an electron in the excited state of Li2+ is :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
In a hydrogen atom, if energy of an electron in ground state is then that in the 2nd excited state (in eV) is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The ionization enthalpy of hydrogen atom is The energy (Joule/mol) required to excite the electron in the atom from
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The velocity (in terms of x) of electron in Bohr’s 3rd orbit of hydrogen is x, then velocity in Bohr’s first orbit of Li2+ is:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The electron in the hydrogen atom undergoes a transition from higher orbitals to an orbital of radius 211.6 pm. This transition is associated with :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Among the following, the energy of 2s orbital is lowest in:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The radius of the orbit of
The expected radius of the
orbit of
is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Assume that the radius of the first Bohr orbit of hydrogen atom is . The radius of the third Bohr orbit of
is _____________ picometer. (Nearest Integer)
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If the radius of the first orbit of hydrogen atom is , then de Broglie’s wavelength of electron in
orbit is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The electron in the $n$th orbit of $\mathrm{Li}^{2+}$ is excited to $(\mathrm{n}+1)$ orbit using the radiation of energy $1.47 \times 10^{-17} \mathrm{~J}$ (as shown in the diagram). The value of $n$ is $\qquad$
Given : $\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \mathrm{~J}$
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The energy of an electron in the first Bohr orbit of hydrogen atom is . Its energy in the third Bohr orbit is__________.
| A. |
|
| B. |
|
| C. |
|
| D. |
|
On transition of an electron of Hydrogen atom from its third permitted energy level to the first level, photons of certain energy was produced. similarly, another transition took place to second permitted energy level from highest permitted energy level. Calculate the ratio of energies of photons produced in the two emissions.
| A. |
|
| B. |
|
| C. |
|
| D. |
|
As per the Bohr model, find the possible values of principal quantum numbers in an electron transition of hydrogen atom from
to
. The time period of an election in the initial state is 27 times the time period of electron in the final state.
| A. |
|
| B. |
|
| C. |
|
| D. |
|
An electron is present in the third orbit of ion, find its angular velocity.
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If the number of revolutions made by electron in $1.0 \mathrm{~s}$ in $\mathrm{H}$ atom in its $n^{\text {th }}$ orbit is twice of the number of revolutions made by electron in $1.0 \mathrm{~s}$ in the $2^{\text {nd }}$ orbit of $\mathrm{He}^{+}$ion atom, then $n$ is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Given below are two statements :
Statement (I) : The orbitals having same energy are called as degenerate orbitals.
Statement (II) : In hydrogen atom, 3p and 3d orbitals are not degenerate orbitals.
In the light of the above statements, choose the most appropriate answer from the options given below :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The value of Rydberg constant $\left(\mathrm{R}_{\mathrm{H}}\right)$ is $2.18 \times 10^{-18} \mathrm{~J}$. The velocity of electron having mass $9.1 \times 10^{-31} \mathrm{~kg}$ in Bohr's first orbit of hydrogen atom $=\ldots \ldots \ldots \times 10^5 \mathrm{~ms}^{-1}$ (nearest integer)
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Electromagnetic radiation of wavelength 663 nm is just sufficient to ionise the atom of metal A. The ionization energy of metal A in kJ mol–1 is _______. (Rounded-off to the nearest integer)
$\left[h=6.63 \times 10^{-34} \mathrm{Js}, C=3.00 \times 10^8 \mathrm{~ms}^{-1}, N_A=6.02 \times 10^{23} \mathrm{~mol}^{-1}\right]$
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The velocity of electrons in second shell of a hydrogen atom is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Correct order of radius at the $I^{\text {st }}$ orbit of $\mathrm{H}, \mathrm{He}^{+}, \mathrm{Li}^{2+}, \mathrm{Be}^{+3}$ is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If the first ionisation energy of H - atom is 13.6 e.v. then the second ionisation energy of $\mathrm{He}^{+}$
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Which of the following is not correct according to Bohr's theory?
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The electron in hydrogen atom is in the first Bohr orbit $(n=1)$. The ratio of transition energies, $E(n=1 \rightarrow n=3)_{\text {to }} E(n=1 \rightarrow n=2)$, is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If the radius of the hydrogen atom is 53 pm, the radius of He+ ion is closest to
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The correct statements among the following
i. $E_2(H)>E_{2 s}(L i)>E_{2 s}(N a)>E_{2 s}(K)$
ii. The maximum number of electrons in the shell with principal quantum number $n$ is equal to $2 n^2$
iii. Extra stability of half-filled subshell is due to smaller exchange energy
iv. Only two electrons,irrespective of their spin,may exist in the same orbital
are
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The radii of the first Bohr orbit of $H\left(r_H\right), H e^{+},\left(r_{H e}^{+}\right)$and $L i^{2+}\left(r_{L i}{ }^{2+}\right)$ are in the border
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Radius of the first excited state of Helium ion is given as : $\mathrm{a}_0 \rightarrow$ radius of first stationary state of hydrogen atom.
| A. |
|
| B. |
|
| C. |
|
| D. |
|
For hydrogen atom, the orbital/s with lowest energy is/are :
(A) 4 s
(B) $3 p_x$
(C) $3 d_{x^2-y^2}$
(D) $3 \mathrm{~d}_{z^2}$
(E) $4 p_z$
Choose the correct answer from the options given below :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n ?
[E : Energy of the stationary state,
Z : atomic number, $\mathrm{n}=$ principal quantum number]
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is________________.
A. $\mathrm{T}_4>\mathrm{T}_3>\mathrm{T}_2>\mathrm{T}_1$
B. The black body consists of particles performing simple harmonic motion.
C. The peak of the spectrum shifts to shorter wavelength as temperature increases.
D. $\frac{T_1}{v_1}=\frac{T_2}{v_2}=\frac{T_3}{v_3} \neq$ constant
E. The given spectrum could be explained using quantisation of energy.
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Find out the quantum 'n' corresponding to excited state of H+ ion if on deexcitation to the ground state that ion emits only two photon in succession with wavelength 1026.7 and 304$A^{\circ}\left(R_H=1.097 \times 10^7 \mathrm{~m}^{-1}\right)$
| A. |
|
| B. |
|
| C. |
|
| D. |
|
In the hydrogen atom, an orbital has a diameter of about 16.92 $A^{\circ}$. What is the maximum number of electrons that can be accommodated?
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The wave function $\psi$ in the Schrodinger wave equation represents:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The energy of an electron in first Bohr orbit of H -atom is -13.6 eV . The magnitude of energy value of electron in the first excited state of $\mathrm{Be}^{3+}$ is _______eV . (nearest integer value)
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Bohr’s theory can also be applied to the ions containing only one electron, similar to that present in hydrogen atom.
