Atoms — Practice

Question 1

Find the energy of the n = 3 level of hydrogen.

Accepted Answer

Apply E_n = -13.6/n squared eV. Answer: -1.51 eV.

Question 2

The Bohr radius is 0.53 x 10^-10 m. Find the radius of the n = 4 orbit.

Accepted Answer

The radius scales as the square of the principal quantum number. Answer: 8.48 x 10^-10 m.

Question 3

The total energy of an electron in a hydrogen orbit is -3.4 eV. Find its kinetic and potential energies.

Accepted Answer

Use K = -E and U = 2E, which hold in every Bohr orbit. Answer: K = +3.4 eV; U = -6.8 eV.

Question 4

Find the wavelength of the photon emitted when a hydrogen atom falls from n = 3 to n = 2.

Accepted Answer

Compute the energy difference from the level formula, then use the 1240 over energy shortcut. Answer: 656 nm, the red Balmer line.

Question 5

To which series does a transition ending on n = 2 belong, and in which region of the spectrum does it lie?

Accepted Answer

Identify the series by its final level and recall which region each occupies. Answer: The Balmer series, in the visible region.

Question 6

An alpha particle of kinetic energy 5.0 MeV is fired head-on at a gold nucleus of Z = 79. Find the distance of closest approach.

Accepted Answer

Equate the kinetic energy to the electrostatic potential energy of the two charges at separation d. Answer: About 4.6 x 10^-14 m.

Question 7

Find the ratio of the orbital periods of the n = 2 and n = 4 levels of hydrogen.

Accepted Answer

Use the fact that the period scales as the cube of the principal quantum number. Answer: 1 to 8.

Question 8

A hydrogen atom in the ground state absorbs a photon and is excited to n = 3. Find the wavelength of the absorbed photon and the number of spectral lines that can then be emitted.

Accepted Answer

Find the energy difference for the absorption, then count the downward transitions available from n = 3. Answer: 102.6 nm; three lines can be emitted.

Question 9

Show that requiring a whole number of de Broglie wavelengths to fit around a Bohr orbit reproduces the angular momentum quantisation condition.

Accepted Answer

Set the circumference equal to n wavelengths and substitute the de Broglie relation. Answer: 2 pi r = n h/(mv) rearranges directly to m v r = n h/(2 pi).

Practice — Atoms

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