Atoms - Physics Lecture Notes

Flashcards covering the introduction to atomic models, Rutherford's scattering experiment, Bohr's postulates, and the line spectra of hydrogen.

Who discovered that atoms contain negatively charged identical constituents called electrons in 1897?

J. J. Thomson

What was the nickname given to J. J. Thomson's 1898 atomic model?

The plum pudding model

According to Thomson's model, how is the positive charge distributed in an atom?

It is uniformly distributed throughout the volume of the atom

Why do rarefied gases emit discrete wavelengths instead of a continuous spectrum?

The average spacing between atoms is large, meaning radiation is due to individual atoms rather than interactions between them

Who obtained the empirical formula for the wavelengths of hydrogen lines in 1885?

Johann Jakob Balmer

Which physicist proposed the 1906 experiment of scattering $\alpha$-particles to investigate atomic structure?

Ernest Rutherford

Which two researchers performed the alpha-particle scattering experiment in 1911?

Hans Geiger and Ernst Marsden

What is the alternative name for Rutherford’s planetary model of the atom?

The nuclear model of the atom

Which radioactive source was used for the beam of $5.5\,MeV$ $\alpha$-particles in the Geiger-Marsden experiment?

$$^{214}_{83}Bi$$

What material and thickness was the thin metal foil used in the Geiger-Marsden experiment?

Gold foil of thickness $2.1 \times 10^{-7}\,m$

What substance made up the screen for the rotatable detector in the alpha-scattering experiment?

Zinc sulphide

What observed phenomenon at the detector indicated the presence of scattered alpha-particles?

Brief light flashes or scintillations

What percentage of incident $\alpha$-particles were found to scatter by more than $1^\circ$?

About $0.14\%$

Approximately how many $\alpha$-particles deflect by more than $90^\circ$ in the scattering experiment?

About $1$ in $8000$

What conclusion did Rutherford draw from the fact that some $\alpha$-particles deflected backwards?

The mass and positive charge of the atom are concentrated tightly at its centre in the nucleus

Rutherford’s experiment suggested the size of the nucleus is in what range?

$10^{-15}\,m$ to $10^{-14}\,m$

What is the known size of an atom based on kinetic theory?

$$10^{-10}\,m$$

Why do atomic electrons not appreciably affect the trajectory of $\alpha$-particles?

Because electrons are very light compared to $\alpha$-particles

What is the charge of an alpha-particle?

Two units of positive charge ($2e$)

What is the atomic number ($Z$) of gold?

79

What is defined as the perpendicular distance of the initial velocity vector of the $\alpha$-particle from the centre of the nucleus?

The impact parameter ($b$)

How does the impact parameter relate to the scattering angle?

An $\alpha$-particle with a small impact parameter suffers large scattering; a large impact parameter results in a small deflection

What happens to an $\alpha$-particle in a head-on collision with a nucleus?

The impact parameter is minimum and the $\alpha$-particle rebounds back ($\theta \approx 180^\circ$)

What is the calculated distance of closest approach ($d$) for a $7.7\,MeV$ $\alpha$-particle to a gold nucleus?

$3.0 \times 10^{-14}\,m$ (or $30\,fm$)

What is the actual observed radius of a gold nucleus?

$$6\,fm$$

In Rutherford's model, what provides the centripetal force ($F_c$) to keep electrons in orbit?

The electrostatic force of attraction ($F_e$) between the revolving electrons and the nucleus

What is the formula for the total energy ($E$) of an electron in a hydrogen atom in Rutherford's model?

$$E = -\frac{e^2}{8\pi\epsilon_0 r}$$

What does the negative sign in the total energy expression of an electron signify?

That the electron is bound to the nucleus

What is the definition of an emission line spectrum?

A spectrum consisting of bright lines on a dark background emitted by an excited atomic gas

What is the definition of an absorption spectrum?

A spectrum containing dark lines corresponding to wavelengths absorbed by a gas when white light passes through it

What is the major stability flaw in the Rutherford model according to classical electromagnetic theory?

An accelerating electron should emit radiation, lose energy, and spiral into the nucleus

According to classical theory, what should happen to the frequency of light emitted by a spiraling electron?

It should change continuously, producing a continuous spectrum instead of the observed line spectrum

Who combined classical and early quantum concepts to form a new atomic theory in 1913?

Niels Bohr

What is Bohr’s first postulate regarding electron orbits?

Electrons can revolve in certain stable orbits (stationary states) without the emission of radiant energy

State Bohr’s second postulate for the quantization of angular momentum.

The electron revolves only in orbits for which orbital angular momentum is an integral multiple of $\frac{h}{2\pi}$

What is the formula for Bohr's third postulate regarding photon emission?

$$h\nu = E_i - E_f$$

What is the value of Planck’s constant ($h$)?

$$6.6 \times 10^{-34}\,J\,s$$

What is the ground state energy of a hydrogen atom in electron volts?

$$-13.6\,eV$$

What is meant by the 'ground state' of an atom?

The lowest energy state of the atom ($n = 1$)

What is the ionization energy of a hydrogen atom?

$$13.6\,eV$$

How much energy is required to excite a hydrogen atom from its ground state to its first excited state ($n = 2$)?

$$10.2\,eV$$

What happens to the spacing between energy levels as the principal quantum number $n$ increases?

The energies of the excited states come closer and closer together

Who provided an explanation for Bohr's second postulate of quantization in 1923?

Louis de Broglie

What condition must be met for a de Broglie particle wave to form a standing wave in a circular orbit?

The circumference must be an integral multiple of wavelengths ($2\pi r_n = n\lambda$)

How is the de Broglie wavelength ($\lambda$) defined for an electron of momentum $p$?

$$\lambda = \frac{h}{p}$$

Name one limitation of the Bohr model.

It is applicable only to hydrogenic atoms and cannot be extended to multi-electron atoms like helium

What are 'hydrogenic atoms'?

Atoms consisting of a nucleus with charge $+Ze$ and a single electron (e.g., $H$, $He^+$, $Li^{2+}$)

Why is Bohr’s model not applicable to many-electron atoms?

It doesn't include the electron-electron electrical forces which are comparable to the electron-nucleus interaction

What energy level corresponds to the state where the electron is completely removed from the nucleus and at rest?

$0\,eV$, where $n = \infty$

In a hydrogen atom, what is the orbital radius of the electron in its ground state?

$$5.3 \times 10^{-11}\,m$$