Atoms

The radius of the first Bohr orbit of hydrogen is 0.529 Å. What is the radius of its second orbit?

The orbital speed of an electron in the first Bohr orbit of hydrogen is 2.2 × 10⁶ m/s. What is its speed in the second orbit?

Calculate the energy of an electron in the third orbit of a hydrogen atom.

What is the ionisation energy of a singly ionised helium atom (He⁺, Z = 2) in its ground state?

Find the energy required to excite a hydrogen atom from its ground state to the first excited state (n = 2).

Calculate the wavelength of the first line (Hα) of the Balmer series of hydrogen. (R = 1.097 × 10⁷ m⁻¹)

An electron in a hydrogen atom is in the n = 4 state. How many spectral lines can be emitted in total as it returns to the ground state through all possible transitions?

Find the shortest wavelength (series limit) of the Lyman series of hydrogen.

Using Bohr's quantization condition, what is the de Broglie wavelength of an electron in the first orbit of hydrogen (r₁ = 0.529 Å)?

The orbital frequency of an electron in the first Bohr orbit of hydrogen is how many times its frequency in the second orbit?

What is the angular momentum of an electron in the third Bohr orbit of hydrogen?

By what factor is the time period of an electron in the second Bohr orbit of hydrogen greater than in the first orbit?

The ionisation potential of a hydrogen-like ion is found to be 54.4 V. What is its atomic number?

Find the second excitation potential of a hydrogen atom (n = 1 to n = 3).

An alpha particle with kinetic energy 5 MeV approaches a gold nucleus (Z = 79) head-on. Estimate its distance of closest approach. (k = 9×10⁹ Nm²/C²)

What is the radius of the ground-state orbit of a doubly ionised lithium atom (Li²⁺, Z = 3)?

An electron transitions from n = 5 to n = 3 in a hydrogen atom. Which spectral series does this belong to, and in what region of the spectrum does it lie?

Calculate the series limit (shortest wavelength) of the Balmer series of hydrogen.