The radius of electron's second stationary orbit in Bohr's atom is $R$ The radius of 3rd orbit will be
- $\frac{ R }{3}$
- $9 R$
- $2.25 R$
- $3 R$
The Correct Option is C
Solution and Explanation
Divide (1) by (2)
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
Top JEE Main Bohr’s Model for Hydrogen Atom Questions
- According to Bohr's theory, the moment of momentum of an electron revolving in the 4th orbit of a hydrogen atom is:
- In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is _____ nm.
(Given $hc = 1245 \, \text{eV nm}, \, e = 1.6 \times 10^{-19} \, \text{C}$). 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 revolves around the nucleus in those orbits for which angular momentum is an integral multiple of Planck’s constant.
In the light of the above statements, choose the most appropriate answer from the options given below:- $\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted energy level to the second level and (ii) the highest permitted energy level to the second permitted level The value of $x$ will be
An electron of a hydrogen like atom, having \(Z=4\), jumps from \(4^{\text {th }}\) energy state to \(2^{\text {nd }}\) energy state. The energy released in this process, will be :
\((\) Given Rch \(=136 eV )\)
Where \(R =\) Rydberg constant
\(c =\) Speed of light in vacuum
\(h =\) Planck's constant
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
Concepts Used:
Bohr's Model of Hydrogen Atom
Niels Bohr introduced the atomic Hydrogen model in 1913. He described it as a positively charged nucleus, comprised of protons and neutrons, surrounded by a negatively charged electron cloud. In the model, electrons orbit the nucleus in atomic shells. The atom is held together by electrostatic forces between the positive nucleus and negative surroundings.
Read More: Bohr's Model of Hydrogen Atom
Bohr's Theory of Hydrogen Atom and Hydrogen-like Atoms
A hydrogen-like atom consists of a tiny positively-charged nucleus and an electron revolving around the nucleus in a stable circular orbit.
Bohr's Radius:
If 'e,' 'm,' and 'v' be the charge, mass, and velocity of the electron respectively, 'r' be the radius of the orbit, and Z be the atomic number, the equation for the radii of the permitted orbits is given by r = n2 ｘr1, where 'n' is the principal quantum number, and r1 is the least allowed radius for a hydrogen atom, known as Bohr's radius having a value of 0.53 Å.
Limitations of the Bohr Model
The Bohr Model was an important step in the development of atomic theory. However, it has several limitations.
- Bohr’s model of the atom failed to explain the Zeeman Effect (effect of magnetic field on the spectra of atoms).
- It failed to explain the Stark effect (effect of electric field on the spectra of atoms).
- The spectra obtained from larger atoms weren’t explained.
- It violates the Heisenberg Uncertainty Principle.