Atoms

When an α-particle of mass 'm' moving with velocity 'v' bombards a heavy nucleus of charge 'Ze', its distance of closest approach from the nucleus depends on m as:

Given the value of Rydberg constant is 10⁷ m⁻¹, the wave number of the last line of the Balmer series in hydrogen spectrum will be:

If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength λ. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be:

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is:

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is:

The radius of the first permitted Bohr orbit for the electron in a hydrogen atom is 0.51 Å and its ground state energy is –13.6 eV. If the electron in hydrogen is replaced by a muon (μ⁻) [charge same as electron, mass 207 mₑ], the first Bohr radius and ground state energy will be:

The total energy of an electron in an atom in an orbit is –3.4 eV. Its kinetic and potential energies are, respectively:

In hydrogen atom, the de Broglie wavelength of an electron in the second Bohr orbit is: [Given Bohr radius a₀ = 52.9 pm]

Let T₁ and T₂ be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to Bohr's model of an atom, the ratio T₁ : T₂ is:

The wavelength of Lyman series of hydrogen atom appears in:

The angular momentum of an electron moving in an orbit of hydrogen atom is 1.5(h/π). The energy in the same orbit is nearly:

The radius of innermost orbit of hydrogen atom is 5.3 × 10⁻¹¹ m. What is the radius of the third allowed orbit of hydrogen atom?

In hydrogen spectrum, the shortest wavelength in the Balmer series is λ. The shortest wavelength in the Brackett series is:

The ground state energy of hydrogen atom is –13.6 eV. The energy needed to ionize hydrogen atom from its second excited state will be:

Given below are two statements: Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum. In the light of the above statements, choose the most appropriate answer from the options given below:

Match List I with List II: List I (Spectral Lines of Hydrogen for transitions from) (A) n₂ = 3 to n₁ = 2 (B) n₂ = 4 to n₁ = 2 (C) n₂ = 5 to n₁ = 2 (D) n₂ = 6 to n₁ = 2 List II (Wavelengths (nm)) (I) 410.2 (II) 434.1 (III) 656.3 (IV) 486.1 Choose the correct answer from the options given below:

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

The de Broglie wavelength of an electron in the n = 2 state of hydrogen atom is close to: (Given Bohr radius = 0.052 nm)

In the Geiger–Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of scattering angle $\theta$. Which option represents the correct plot?

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 eV = 1.6 × 10⁻¹⁹ J, e = 1.6 × 10⁻¹⁹ C and 1/(4πε₀) = 9 × 10⁹ N m²/C²)

An electron is revolving in an excited state of a Hydrogen atom with velocity $\sqrt{25.6}\times10^{5}\,\text{ms}^{-1}$. The radius of the orbit is $x\times10^{-9}\,$m. The value of $x$ is: [$m_e=9\times10^{-31}\,$kg, $e=-1.6\times10^{-19}\,$C, $\dfrac{1}{4\pi\varepsilon_0}=9\times10^{9}\,\text{Nm}^2\text{C}^{-2}$]