Atoms and Nuclei

In hydrogen atom, transition from the state $\mathrm{n}=6$ to $n=1$ results in ultraviolet radiation. Infrared radiation will be obtained in the transition

Out of the following transitions in hydrogen atom, identify the transition which emits photons of highest frequency.

${ }_{88} \mathrm{R}_{\mathrm{a}}^{226}$ is converted into ${ }_{82} \mathrm{P}_{\mathrm{b}}^{206}$ by emission of alpha ( $\alpha$ ) and beta ( $\beta$ ) particles. The number of alpha and beta particles emitted are respectively

A radioactive element A decays into radioactive element C by the following processes in succession.
$\mathrm{A} \rightarrow \mathrm{B}+{ }_2 \mathrm{H}_{\mathrm{e}}^4 ; \mathrm{B} \rightarrow \mathrm{C}+2 \mathrm{e}^{-}$Then elements

Which of the following transitions in hydrogen atom emit photons of highest frequency? ( $\mathrm{n}=$ principle quantum number)

Two radioactive materials $A$ and $B$ having decay constant ' $7 \lambda$ ' and ' $\lambda$ ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is

Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is ( $h=$ Planck's constant, $\mathrm{I}=$ moment of inertia of diatomic molecule)

$$ \begin{aligned} &\text { For the following reaction, the particle ' } \mathrm{x} \text { ' is }{ }_6 \mathrm{C}^{11}\longrightarrow{ }_5 \mathrm{~B}^{11}+\beta+\mathrm{X} \end{aligned} $$

In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is

In hydrogen atom spectrum, when an electron jumps from second excited state to the first excited state, the wavelength of radiation emitted is ' $\lambda$ '. If the electron jumps from the third excited state to the second orbit, the wavele...

The ratio of angular momentum of an electron in $\mathrm{n}^{\text {th }}$ orbit of hydrogen atom to the velocity of electron in $\mathrm{n}^{\text {th }}$ orbit is proportional to

If ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths of the first member of the Balmer and Paschen series, in hydrogen atom respectively, then the ratio of respective frequencies, $f_1 / f_2$, is

The ratio of the wavelength of the last line of Paschen series to that of Balmer series is

The frequency of revolution of an electron in the $\mathrm{n}^{\text {th }}$ orbit of hydrogen atom is

In hydrogen atom, ratio of the shortest wavelength in the Balmer series to that in the Paschen series is

According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series will be

When a hydrogen atom is raised from the ground state to the excited state

In hydrogen atom, if $\mathrm{V}_{\mathrm{n}}$ and $\mathrm{V}_{\mathrm{p}}$ are orbital velocities in $\mathrm{n}^{\text {th }}$ and $\mathrm{p}^{\text {th }}$ orbit respectively, then the ratio $\mathrm{V}_{\mathrm{p}}: \mathrm{V}_{\mathr...

The spectral series observed for hydrogen atom found in visible region is

For hydrogen atom, ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ' $\lambda_1$ ' and ' $\lambda_2$ ' is $\frac{x}{32}$. The value of ' $x$ ' is...

Half-lives of two radioactive elements A and B are 30 minute and 60 minute respectively. Initially the samples have equal number of nuclei. After 120 minute the ratio of decayed numbers of nuclei of $B$ to that of $A$ will be

The ratio of minimum wavelengths of Lyman and Balmer series will be

If ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths of the first line of the Lyman and Paschen series respectively, then $\lambda_2: \lambda_1$ is

In the uranium radioactive series, the initial nucleus is ${ }_{92}^{238} \mathrm{U}$ and that the final nucleus is ${ }_{82}^{206} \mathrm{~Pb}$. When uranium nucleus decays into lead, the number of $\alpha$-particles and $\beta$-particles...

A diatomic molecule has moment of inertia ' I ', By applying Bohr's quantization condition, its rotational energy in the $\mathrm{n}^{\text {th }}$ level is $[\mathrm{n} \geq 1]$ [h= Planck's constant]

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

In the third orbit of hydrogen atom the energy of an electron ' $E$ '. In the fifth orbit of helium $(Z=2)$ the energy of an electron will be

The radius of innermost orbit of hydrogen atom is $5.3 \times 10^{-11} \mathrm{~m}$. The radius of fourth allowed orbit of hydrogen atom is

An electron of stationary Hydrogen atom passes from fifth energy level to ground level. The velocity that the atom acquired as a result of photo emission is
( $\mathrm{m}=$ mass of electron, $\mathrm{R}=$ Rydberg's constant)
( $\mathrm{h}=$...

Which of the following statements about the Bohr model of the hydrogen atom is false?

Frequency of the series limit of Balmer series of hydrogen atom of Rydberg's constant ' $R$ ' and velocity of light ' $C$ ' is

When an electron orbiting in hydrogen atom in its ground state jumps to higher excited state, the de-Broglie wavelength associated with it

In $\mathrm{M}_{\mathrm{O}}$ is the mass of an oxygen isotope ${ }_8 \mathrm{O}^{17}$ and $\mathrm{M}_{\mathrm{p}}$ and $\mathrm{M}_{\mathrm{N}}$ are the mass of proton and mass of neutron respectively, then the nucleus binding energy of th...

Two radioactive substances A and B have decay constants ' $5 \lambda$ ' and ' $\lambda$ ' respectively. At $\mathrm{t}=0$, they have the same number of nuclei. The ratio of number of nuclei of $A$ to those of $B$ will be $\left(\frac{1}{\ma...

In the second orbit of hydrogen atom, the energy of an electron is ' $E$ '. In the third orbit of helium atom, the energy of the electron will be (atomic number of helium $=2$)

A radioactive substance has half-life of 60 minute. During 3 hour, the amount of substance decayed would be

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

Acceleration of an electron in the first Bohr's orbit is proportional to $\mathrm{m}=$ mass of electron, $\mathrm{r}=$ radius of the orbit, $\mathrm{h}=$ Planck's constant)

In the given reaction
\({ }_z \mathrm{X}^A \rightarrow{ }_{z+1} \mathrm{Y}^A \rightarrow{ }_{z-1} \mathrm{~K}^{A-4} \rightarrow{ }_{z-1} \mathrm{~K}^{\mathrm{A}-4}\)
radioactive radiations are emitted in the sequence

If 'T' is the half life of a radioactive substance then its instantaneous rate of change of activity is proportional to

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (a) second to first energy level and (b) highest energy level to second level is

The angular momentum of the electron in the third Bohr orbit of hydrogen atom is ' $l$ '. Its angular momentum in the fourth Bohr orbit is

In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is

If the ionisation energy for the hydrogen atom is 13.6 eV , then the energy required to excite it from the ground state to the next higher state is nearly

Using Bohr's model, the orbital period of electron in hydrogen atom in $\mathrm{n}^{\text {th }}$ orbit is ( $\mathrm{m}=$ mass of electron, $\mathrm{h}=$ Planck's constant, $\mathrm{e}=$ electronic charge, $\varepsilon_0=$ permittivity of ...

In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' $r_0$ ' is the radius of the ground state orbit, ' $m$ ' is the mass, ' e ' is the charge on the elec...

Radius of first orbit in H -atom is ' $a_0$ ' Then, de-Broglie wavelength of electron in the third orbit is

If an electron in a hydrogen atom jumps from an orbit of level \(n=3\) to orbit of level \(n=2\), then the emitted radiation frequency is (where R = Rydberg's constant, C = Velocity of light)

For an electron moving in the \(\mathrm{n}^{\text {th }}\) Bohr orbit the deBroglie wavelength of an electron is

The ratio of wavelengths for transition of electrons from \(2^{\text {nd }}\) orbit to \(1^{\text {st }}\) orbit of Helium \(\left(\mathrm{He}^{++}\right)\) and Lithium \(\left(\mathrm{Li}^{++1}\right)\) is (Atomic number of Helium \(=2\), ...