Atoms practice · Mixed difficulty

In the Bohr model of hydrogen atom, the electron is treated as a particle going in a circle with the centre at the proton. The proton itself is assumed to be fixed in an inertial frame. The centripetal force is provided by the Coloumb attraction. In the ground state, the electron goes round the proton in a circle of radius $5.3 \times 10^{-11} \mathrm{~m}$. Find the speed of the electron in the ground state. Mass of the electron $=9.1 \times 10^{-31} \mathrm{~kg}$ and charge of the electron $=1.6 \times 10^{-19} \mathrm{C}$.

Which of the following statements is/are correct regarding $X$-ray tube?

In vacuum an electron of energy $10\;keV$ hits tungsten target, then emitted radiation will be

Assertion (A): In the Balmer series of hydrogen spectrum as wavelength increases the spectral lines becomes closer.

Reason (R): For higher orbits energy gap between them decreases.

$\mathrm{N}^{\text {th }}$ level of $\mathrm{Li}^{2+}$ has the same energy as the ground state energy of the hydrogen atom. If $r_N$ and $r_1$ is the radii of the $\mathrm{N}^{\text {th }}$ Bohr orbit of $\mathrm{Li}^{2+}$ and $\mathrm{H}$ atom respectively, then the ratio $r_N / r_1$ is

What do you understand by the phrase “ground state atom”?

In separate experiments, four different particles each start from far away with the same speed and impinge directly on a gold nucleus. The masses and charges of the particles are

particle 1: mass ${m}_0$, charge ${q}_0$

particle 2: mass $2{~m}_0$, charge $2{q}_0$

particle 3: mass $2{~m}_0$, charge ${q}_0 / 2$

particle 4: mass ${m}_0 / 2$, charge $2{q}_0$

Rank the particles according to the distance of closest approach to the gold nucleus, from smallest to largest.

Assertion (A): Crystalline solids can cause X-rays to diffract.

Reason (R): Interatomic distance in crystalline solids is of the order of $0.1 \mathrm{~nm}$.

Assertion: For revolving electron, direction of angular momentum and magnetic moment are opposite.
Reason: Charge of electron is negative.

The ratio of the longest to shortest wavelengths in Lyman series of hydrogen spectra is

When $X$ rays pass through a strong uniform magnetic field. Then they

In a Rutherford scattering experiment when a projectile of charge $\mathrm{Z}_1$ and mass $\mathrm{M}_1$ approaches a target nucleus of charge $\mathrm{Z}_2$ and mass $\mathrm{M}_2$, the distance of closest approach is $\mathrm{r}_0$. The energy of the projectile is

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 the wavelengths of radiations corresponding to transitions $C$ to $B$, $B$ to $A$ and $C$ to $A$ respectively, then which of the following relations is correct?

In any Bohr orbit of the hydrogen atom, the ratio of kinetic energy to potential energy of the electron is

The relation between magnetic moment $\mu$ of a revolving electron around the nucleus with principal quantum number $n$ is

Assertion (A): Laser is used to measure distant object as moon.

Reason (R): Lasers are highly coherent source of light.

The value of angular momentum for $\mathrm{He}^{+}$ ion in the first Bohr orbit is:

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

The specific charge of an electron is

In Rutherford scattering experiment, what will be the correct angle for $\alpha -$ scattering for an impact parameter b = 0

For which one of the following Bohr model is not valid

Stopping potentials of $24,100,110,115 \mathrm{kV}$ are measured for photoelectrons emitted from a certain element when it is irradiated with monochromatic X-rays. The element is used as a target in an $\mathrm{X}$-ray tube. The energy of $\mathrm{K}$ line is -

Consider a photon of continuous $\mathrm{X}$-ray and a photon of characteristics $\mathrm{X}$-ray of the same wavelength. Which of the following is different for the two photons:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The beam of electrons show wave nature and exhibit interference and diffraction.
Reason R : Davisson Germer Experimentally verified the wave nature of electrons.
In the light of the above statements, choose the most appropriate answer from the options given below:

Calculate the value of 'fine structure constant'.

Mosley measured the frequency $\left( f \right)$ of the characteristic $X$-rays from many metals of different atomic number $\left( \mathrm{Z} \right)$ and represented his results by a relation known as Mosley’s law. This law is (a, b are constants)

$\mathrm{N}^{\text {th }}$ level of $\mathrm{Li}^{2+}$ has the same energy as the ground state energy of the hydrogen atom. If $r_N$ and $r_1$ is the radii of the $\mathrm{N}^{\text {th }}$ Bohr orbit of $\mathrm{Li}^{2+}$ and $\mathrm{H}$ atom respectively, then the ratio $r_N / r_1$ is

STATEMENT-1:If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic $\mathrm{X}$-rays do not change.

STATEMENT-2:When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into $\mathrm{X}$-ray energy.

The order of the size of nucleus and Bohr radius of an atom respectively are

An X-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times {10^{ - 2}}\mathrm{A}.$

The maximum energy of a photon in the radiation in eV is $h = 6.62 \times {10^{ - 34}}$ Js ,

$c = 3 \times {10^8}\;\mathrm{m}{\mathrm{s}^{ - 1}})$