Atoms practice · Mixed difficulty

Which of the following statements are true regarding Bohr’s model of hydrogen atom

(I) Orbiting speed of electron decreases as it shifts to discrete orbits away from the nucleus

(II) Radii of allowed orbits of electron are proportional to the principal quantum number

(III) Frequency with which electrons orbit around the nucleus is discrete orbits is inversely proportional to the cube of principal quantum number

(IV) Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits

Select correct answer using the codes given below

A particle moving with a velocity of $\frac{1}{{100}}\mathrm{th}$ of that of light will cross a nucleus on about

A hydrogen atom is in ground state absorbs a photon of ultraviolet radiation of wavelength $50 \mathrm{~nm}$. Assuming that the entire photon energy is taken up by electron with what KE will the electron be emitted.

In a spectrum of hydrogen atom, the ratio of shortest wavelength in Lyman series to longest wavelength in Paschen series is

When the wave of hydrogen atom comes from infinity into the first orbit then the value of wave number is

To explain his theory, Bohr used

Assertion (A): Between any two given energy levels, the number of absorption transitions is always less than or equal to the number of emission transitions.

Reason (R): Absorption transitions start from the lowest energy level only and may end at any higher energy level. But emission trasitions may start from any higher energy level and end at an energy level below it.

Stopping potentials of $24,100,110$ and $115 \mathrm{~kV}$ are measured for photoelectrons emitted from a certain element when it is irradiated with monochromatic ${X}$-rays. If this element is used as a target in an $X$-ray tube, what will be the wavelength of $K_\alpha$ line? Assume that photons have sufficient energy to excite electrons of all the energy levels. $\left[hc=12.4 \times 10^3 \,\mathrm{eV} . \mathop A\limits^ \circ\right]$

For characteristic $X$-ray of some material

Statement-1: When hydrogen atom is raised from the ground state to an excited state the kinetic energy increases.
Statement-2: The velocity of electron in a quantum state is inversely proportional to the quantum number of the state.

An elementary particle of mass $m$ and charge $+ e$ is projected with velocity $v$ at a much more massive particle of charge $Ze,$ where $Z > 0.$ What is the closest possible approach of the incident particle

In the Bohr’s hydrogen atom model, the radius of the stationary orbit is directly proportional to ($n =$ principle quantum number)

The most penetrating radiation out of the following is

What will be the angular momentum of an electron, if energy of this electron in $H$-atom is $- 1.5\,\,eV$ (in $J$-$s$)

The spectral series of the hydrogen spectrum that lies in the ultraviolet region is the

The energy of the characteristic X-ray photon in Coolidge tube comes from

Particles used in the Rutherford's scattering experiment to deduce the structure of atoms

Energy of electron in an orbit of $H$-atom is

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $x \times 10^{15} \mathrm{~Hz}$. The value of $x$ is_____

(Given $h=4.25 \times 10^{-15} \mathrm{eVs}$ )

Assuming that all the transitions are possible, consider the optical spectrum $3800 \mathop A\limits^ \circ$ to $7700 \mathop A\limits^ \circ$. No. of lines of hydrogen as compared to doubly ionized lithium will be:

Which of the following is true for number of spectral lines in going from Lyman series to $P$-fund series

Which of the following is not the property of cathode rays?

In Raman effect, Stoke’s lines are spectral lines having

The voltage applied across an X-ray tube is nearly equal to

Given below are two statements:

Statement 1: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model.

Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.

In the light of the above statements, choose the most appropriate from the options given below

In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as $F=\frac{e^2}{4 \pi \varepsilon_0}\left(\frac{1}{r^2}+\frac{\beta}{r^3}\right)$, where $\beta$ is a constant. For this atom, the radius of the $n$th orbit in terms of the Bohr's radius $\left(a_0=\frac{\varepsilon_0 h^2}{m \pi e^2}\right)$ is

If an element with principal quantum number ${n}>4$ were not allowed in nature, the number of possible elements would be :-

According to Bohr's theory, the moment of momentum of an electron revolving in $4^\text{th}$ orbit of hydrogen atom is:

A $X$-ray tube is working at a potential difference of $20 \,\mathrm{kV}$. The potential difference is decreased to $10 \,\mathrm{kV}$. It is found that difference of the wavelength of $K_\alpha \,{X}$-ray and the most energetic continuous ${X}$-ray becomes 4 times of the difference prior to the change of voltage. Find the atomic number of the target element.

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.