What does the presence of discrete lines in an atomic spectrum indicate about the energy levels of electrons in an atom?

First Bohr radius of an atom with $Z = 82$ is $R$. Radius of its third orbit is

The distance of closest approach of an $\alpha$-particle fired towards a nucleus with momentum $p$, is $r$. If the momentum of the $\alpha$-particle is $2p$, the corresponding distance of closest approach is

If the wavelength of the first line of the Balmer series of hydrogen is $6561 \, \mathop {ext{A}}\limits^ \circ ,$ the wavelength of the second line of the series should be

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths ${\lambda _1}:{\lambda _2}$ emitted in the two cases is

The energy of an electron in a hydrogen atom is given by $E_n = -\frac{13.6}{n^2}$ eV. What is the energy required to ionize a hydrogen atom from its ground state?

Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr’s atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength $\lambda$ (given in terms of the Rydberg constant $R$ for the hydrogen atom) is equal to

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

The energy of a hydrogen atom in the ground state is $- 13.6\,\,eV$. The energy of a $H{e^ + }$ ion in the first excited state will be

Which of the following statements is TRUE regarding the electrical neutrality of atoms?

(A) Atoms are electrically neutral because they have an equal number of neutrons and protons.

(B) Atoms are electrically neutral because they have an equal number of protons and electrons.

(C) Atoms are always electrically neutral, regardless of the number of subatomic particles.

(D) Atoms can be positively or negatively charged depending on the element.

The energy of electron in the nth orbit of hydrogen atom is expressed as${E_n} = \frac{{ - 13.6}}{{{n^2}}}eV$. The shortest and longest wavelength of Lyman series will be