Atoms

A hydrogen atom in its first excited state absorbs a photon of energy $x\times10^{-2}$ eV and excited to a higher energy state where the potential energy of electron is $-1.08$ eV. The value of $x$ is ______.

The momentum of an electron revolving in n$^{\text{th}}$ 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 :

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda$. The value of principal quantum number 'n' of the excited state will be : (R : Rydberg constant)

$\dfrac x{x+4}$ 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 ______.

In the hydrogen spectrum, $\lambda$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "$a\lambda$" between the wavelength of 3$^{\text{rd}}$ transition line of Paschen series and that of 2$^{\text{nd}}$ transition line of Balmer series where $a=$ ______.

Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

Using Bohr 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:

A nuclear physicist performed an experiment on the scattering of alpha particles by thin metal foil of gold. The alpha particles were accelerated up to kinetic energy 3.2 Mev. The estimation of the radius of the nucleus of gold element (Z = 79) by him is _______ $\times10^{-16}$ m

(Take $\dfrac1{4\pi\epsilon_o}=9\times10^9$ N m$^2$/C$^2$)

Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.

The transitions A, B and C respectively represent :

A particle of mass $m$ moves in circular orbits with potential energy $V(r) = Fr$, where $F$ is a positive constant and $r$ is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by $R$ and its speed and energy are denoted by $v$ and $E$, respectively, then for the $n^{\text{th}}$ orbit (here $h$ is the Planck's constant)

In an X-ray tube, electrons emitted from a filament (cathode) carrying current $I$ hit a target (anode) at a distance $d$ from the cathode. The target is kept at a potential $V$ higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current $I$ is decreased to $\dfrac I2$, the potential difference $V$ is increased to $2V$, and the separation distance $d$ is reduced to $\dfrac d2$, then

A free hydrogen atom after absorbing a photon of wavelength $\lambda_a$ gets excited from the state $n = 1$ to the state $n = 4$. Immediately after that the electron jumps to $n = m$ state by emitting a photon of wavelength $\lambda_e$. Let the change in momentum of atom due to the absorption and the emission are $\Delta p_a$ and $\Delta p_e$, respectively. If $\lambda_a/\lambda_e = \frac15$, which of the option(s) is/are correct?

[Use $hc = 1242$ eV nm; 1 nm $= 10^{-9}$ m, $h$ and $c$ are Planck's constant and speed of light, respectively]

Consider a hydrogen-like ionized atom with atomic number $Z$ with a single electron. In the emission spectrum of this atom, the photon emitted in the $n = 2$ to $n = 1$ transition has energy 74.8 eV higher than the photon emitted in the $n = 3$ to $n = 2$ transition. The ionization energy of the hydrogen atom is 13.6 eV. The value of $Z$ is __________.

An electron in a hydrogen atom undergoes a transition from an orbit with quantum number $n_i$ to another with quantum number $n_f$. $V_i$ and $V_f$ are respectively the initial and final potential energies of the electron. If $\frac{V_i}{V_f} = 6.25$, then the smallest possible $n_f$ is

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If $\lambda_{min}$ is the smallest possible wavelength of X-ray in the spectrum, the variation of $\log\lambda_{min}$ with log V is correctly represented in :

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r=\lambda_1/\lambda_2$, is given by :

According to Bohr's theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the n$^{\text{th}}$ orbit is proportional to : (n = principal quantum number)

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :