Constituents of the atom：練習問題

Which of the following is the correct value for the ratio of the specific charge of a proton to the specific charge of an alpha particle (\(^{4}_{2}He\))?
Assume the mass of a neutron is equal to the mass of a proton.

Which of the following statements regarding Rutherford's alpha-particle scattering experiment provides the most direct evidence for the existence of a small, massive, positively charged nucleus?

A specific ion has a charge of \( +4.8 \times 10^{-19} \text{ C} \) and a specific charge of \( 3.1 \times 10^{7} \text{ C kg}^{-1} \). Which of the following is most likely to be the nucleus of this ion?
Take \( 1u = 1.66 \times 10^{-27} \text{ kg} \) and \( e = 1.60 \times 10^{-19} \text{ C} \).

Two isotopes of the same element are ionized. Ion X is \( ^{35}_{17}\text{Cl}^{+} \) and Ion Y is \( ^{37}_{17}\text{Cl}^{+} \).

Which of the following correctly compares the specific charge of Ion X to Ion Y?

In a head-on collision between an alpha particle (mass \( m_{α} \), charge \( +2e \)) and a stationary nucleus (mass \( M \), charge \( +Ze \)), the alpha particle comes to rest at a distance \( d \) from the center of the nucleus. If the experiment is repeated with a nucleus of the same mass but half the proton number, and the initial kinetic energy is halved, what is the new distance of closest approach?

Calculate the specific charge of a lithium-7 nucleus, \({}^{7}_{3}Li\), in SI units.

In the Rutherford scattering experiment, most alpha particles passed through the gold foil with negligible deflection. State the conclusion drawn from this observation regarding the structure of the atom.

Determine the ratio of the specific charge of a hydrogen nucleus (proton) to the specific charge of an alpha particle.

(a) Define the term specific charge of a particle and state its SI unit.

(b) A lithium ion, \(^{7}_{3}Li^{+}\), is formed by removing one electron from a neutral lithium atom. Calculate the specific charge of this lithium ion.
Assume the mass of a nucleon is \(1.67 \times 10^{-27}\) kg and the elementary charge is \(1.60 \times 10^{-19}\) C.

(c) Briefly explain how the results of the Rutherford alpha-particle scattering experiment provided evidence for the existence of a small, massive, and positively charged nucleus.

(a) Radium-226 (\(^{226}_{88}Ra\)) decays into Radon (Rn) by emitting an alpha particle. Write the complete nuclear equation for this decay.

(b) Calculate the radius of a Radium-226 nucleus.
Use \(R_{0} = 1.25 \times 10^{-15}\) m.

(c) Using the relationship \(R = R_{0}A^{1/3}\), show that the density of nuclear matter is independent of the nucleon number \(A\). Assume the mass of a nucleus is approximately \(A \times u\), where \(u\) is the atomic mass unit.