Atoms and Nuclei

The wavelength of light for the least energetic photons emitted in the Lyman series of the hydrogen spectrum is nearly [Take \(\mathrm{hc}=1240 ~\mathrm{eV}\) - \(\mathrm{nm}\), change in energy of the levels \(=10.2 ~\mathrm{eV}\) ]

The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number '\(n\)' as

Magnetic field at the centre of the hydrogen atom due to motion of electron in \(\mathrm{n}^{\text {th }}\) orbit is proportional to

If the radius of the first Bohr orbit is '\(r\)' then the de-Broglie wavelength of the electron in the \(4^{\text {th }}\) orbit will be

Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light (c) is

Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

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

An isotope of the original nucleus can be formed in a radioactive decay, with the emission of following particles.

A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be

When an electron is excited from its 4 th orbit to 5 th stationary orbit, the change in the angular momentum of electron is approximately.
(Planck's constant \(=h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}\) )

An excited hydrogen atom emits a photon of wavelength \(\lambda\) in returning to ground state. The quantum number \(n\) of the excited state is (\(R=\) Rydberg's constant)

The wavelength of radiation emitted is '\(\lambda_0\)' when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen ...

In Lyman series, series limit of wavelength is \(\lambda_1\). The wavelength of first line of Lyman series is \(\lambda_2\) and in Balmer series, the series limit of wavelength is \(\lambda_3\). Then the relation between \(\lambda_1\), $$\l...

In Balmer series, wavelength of the \(2^{\text {nd }}\) line is '\(\lambda_1\)' and for Paschen series, wavelength of the \(1^{\text {st }}\) line is '\(\lambda_2\)', then the ratio '\(\lambda_1\)' to '\(\lambda_2\)' is

Two different radioactive elements with half lives '\(\mathrm{T}_1\)' and '\(\mathrm{T}_2\)' have undecayed atoms '\(\mathrm{N}_1\)' and '\(\mathrm{N}_2\)' respectively present at a given instant. The ratio of their activities at that insta...

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time \(t=\frac{1}{2 \lambda}\) is [\(\lambda=\) decay constant]

An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage change in the speed of electron?

The orbital magnetic moment associated with orbiting electron of charge '\(e\)' is

Bohr model is applied to a particle of mass '\(\mathrm{m}\)' and charge '\(\mathrm{q}\)' moving in a plane under the influence of a transverse magnetic field '\(B\)'. The energy of the charged particle in the \(\mathrm{n}^{\text {th }}\) le...

According to Bohr's theory of hydrogen atom, the total energy of the electron in the \(\mathrm{n}^{\text {th }}\) stationary orbit is

The ratio of longest to shortest wavelength emitted in Paschen series of hydrogen atom is

The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number \(\mathrm{z}\). The value of \(\mathrm{z}\) is

The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of hydrogen atom is

The wave number of the last line of the Balmer series in hydrogen spectrum will be
(Rydberg's constant \(=10^7 \mathrm{~m}^{-1}\) )

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

The ratio of maximum to minimum wavelength in Balmer series of hydrogen atom is

An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?

The half life of a radioactive substance is 30 minute. The time taken between 40% decay and 85% decay of the same radioactive substance is

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

The energy of an electron in the excited hydrogen atom is \(-3.4 \mathrm{~eV}\). Then according to Bohr's theory, the angular momentum of the electron in that excited state is (\(\mathrm{h}=\) Plank's constant)

The shortest wavelength for Lyman series is 912 \(\mathop A\limits^o\). The longest wavelength in Paschen series is

In the Bohr model, an electron moves in a circular orbit around the nucleus. Considering an orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in nth excited state, is
(e = electr...

Energy of electron in the second orbit of hydrogen atom is \(\mathrm{E}\). The energy of electron '\(\mathrm{E}_3\)' in the third orbit of helium \((\mathrm{He})\) atom will be

A nucleus breaks into two nuclear parts, which have their velocity ratio \(2: 1\). The ratio of their nuclear radii will be

In \(n^{\text {th }}\) Bohr orbit, the ratio of the kinetic energy of an electron to the total energy of it, is

Two radioactive materials \(X_1\) and \(X_2\) have decay constants '\(5 \lambda\)' and '\(\lambda\)' respectively. Initially, they have the same number of nuclei. After time '\(t\)', the ratio of number of nuclei of \(X_1\) to that of $$\ma...

If '\(E\)' and '\(L\)' denote the magnitude of total energy and angular momentum of revolving electron in \(\mathrm{n}^{\text {th }}\) Bohr orbit, then

'\(\lambda_1\)' is the wavelength of series limit of Lyman series, '\(\lambda_2\)' is the wavelength of the first line line of Lyman series and '\(\lambda_3\)' is the series limit of the Balmer series. Then the relation between $$\lambda_1,...

When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes

Ratio centripetal acceleration for an electron revolving in 3rd and 5th Bohr orbit of hydrogen atom is

If the electron in a hydrogen atom moves from ground state orbit to 5th orbit, then the potential energy of the electron

The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are

The gyromagnetic ratio of an electron in an hydrogen atom, according to Bohr model is

The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength or the particle in the regions \(0 \leq x \leq 1\) and \(x > 1\) are \(\lambda_1\) and \(\lambda_2\) respectively. II the total ...

A sample of radioactive element contains \(8 \times 10^{16}\) active nuclei. The halt-life of the element is 15 days. The number of nuclei decayed after 60 days is

The energy levels with transitions for the atom are shown. The transitions corresponding to emission of radiation of maximum and minimum wavelength are respectively

Using Bohr's model, the orbital period of electron in hydrogen atom in $n$th orbit is ( $\varepsilon_0=$ permittivity of free space, $h=$ Planck's constant, $m=$ mass of electron and $\theta=$ electronic charge)

The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number \(n\) as

The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light \((c)\) is ( \(h=\) Planck's constant, \(\varepsilon_0=\) permittivity of free space, \(e=\) charge on electron)

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? (\(I=\) moment of inertia of diatomic molecule and, \(h=\) Planck's constant)