Atoms PYQs

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 $r$ of the $n^{th}$ orbit and the particle’s speed $v$ in the orbit depend on $n$ as

Energy and radius of first Bohr orbit of $\mathrm{He}^+$ and $\mathrm{Li}^{2+}$ are given.

Match List I with List II. Choose the correct answer from the options given below:

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:

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

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

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

If radius of second Bohr orbit of the He+ ion is 105.8 pm, what is the radius of third Bohr orbit of of third Bohr orbit of Li²⁺ ion?

For which one of the following, Bohr model is not valid?

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

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

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

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

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

Hydrogen atom in ground state is excited by a monochromatic radiation of λ = 975 Å. Number of spectral lines in the resulting spectrum emitted will be:

Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is

The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:

Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model?

The electron in the hydrogen atom jumps from excited state (n = 3) to its ground state (n = 1) and the photons thus emitted irradiate a photosensitive material. If the work function of the material is 5.1 eV, the stopping potential is estimated to be (the energy of the electron in nth state Eₙ = −(13.6 / n² eV))

The ionization energy of the electron in hydrogen atom in its ground state is $13.6\,\text{eV}$. The atoms are excited to higher energy levels to emit radiations of 6 wavelengths. Maximum wavelength corresponds to transition between:

The ground state energy of hydrogen atom is -13.6 eV. When its electron is in the first excited state, its excitation energy is

Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emitted by hydrogen will be:

Energy levels $A$, $B$ and $C$ of a certain atom correspond to increasing values of energy, i.e. $E_A < E_B < E_C$. If $\lambda_1$, $\lambda_2$ and $\lambda_3$ are wavelengths of radiations corresponding to transitions $C \to B$, $B \to A$ and $C \to A$ respectively, which of the following relations is correct?

The total energy of an electron in the first excited state of hydrogen is about $-3.4\,\text{eV}$. Its kinetic energy in this state is: