Atomic and Nuclear Physics: One Mark Questions, Book Back Answers and Notes

About Atomic and Nuclear Physics

Hard ~120 min study

This unit answers two questions: what is inside an atom, and what is inside its nucleus? Each answer came from an experiment, and the textbook follows them in order. That makes the unit easier to remember as a story than as a list of formulas.

Gas discharge tubes gave cathode rays, which turned out to be electrons. Thomson measured their specific charge using electric and magnetic fields, and Millikan measured the charge itself. Rutherford's alpha scattering experiment showed that the positive charge and most of the mass sit in a tiny nucleus. Bohr then explained why the atom is stable and why hydrogen gives sharp spectral lines. After that the focus moves to the nucleus, where mass defect and binding energy explain stability, radioactivity and nuclear energy.

The unit mixes theory with numericals. Expect problems on Bohr radius and energy levels, wavelengths of spectral lines, binding energy from mass defect, and half-life. In answers, state the postulates clearly and show units at each step, especially when converting mass in u to energy in MeV.

What you'll learn

• List the properties of cathode rays and explain how they showed the existence of the electron.
• Calculate the specific charge and mass of the electron from Thomson's and Millikan's experiments.
• State the postulates and limitations of Bohr's atom model.
• Calculate energies and wavelengths for spectral lines of the hydrogen atom.
• Calculate the mass defect and binding energy of a nucleus.
• Use the law of radioactive decay to solve half-life and mean life problems.
• Compare nuclear fission and fusion and describe where each is used.

Before you start

• Newton's laws of motion and circular motion.
• Electrostatics and Coulomb's law.
• Photon energy E = hν from the dual nature unit.

Atomic and Nuclear Physics explained

From the Electron to the Nucleus

Discovery of the Electron

When a high voltage is applied across a gas at very low pressure, rays leave the cathode. These cathode rays travel in straight lines, carry negative charge and are deflected by electric and magnetic fields. J.J. Thomson passed them through crossed electric and magnetic fields, adjusted the fields so there was no deflection, and found the specific charge $e/m$ to be about $1.7 \times 10^{11}$ C kg⁻¹. The value was the same for every cathode material and gas. Millikan's oil drop experiment then measured the charge on tiny oil drops and found it was always a whole-number multiple of $1.6 \times 10^{-19}$ C. This showed that charge is quantised, and combining e with e/m gave the mass of the electron.

Atomic Models

Thomson's model pictured the atom as a sphere of positive charge with electrons embedded in it. Rutherford's alpha scattering experiment disproved this. Most alpha particles passed straight through a gold foil, but a few bounced back, which showed a tiny, dense, positive nucleus. Rutherford's model had a flaw: an electron moving in a circle is accelerating, so by classical theory it should radiate energy and spiral into the nucleus. Bohr solved this by allowing electrons only in orbits where angular momentum is $\frac{nh}{2\pi}$. In these orbits the electron does not radiate. It emits or absorbs energy only when it jumps from one orbit to another.

Hydrogen Spectrum

For hydrogen, Bohr's theory gives orbit radii $r_n = 0.529\, n^2$ Å and energies $E_n = -\frac{13.6}{n^2}$ eV. When an electron drops from a higher level to a lower one, it emits a photon of energy equal to the difference. For example, the jump from n = 2 to n = 1 gives 10.2 eV. Jumps ending at n = 1 form the Lyman series (ultraviolet), and jumps ending at n = 2 form the Balmer series (visible). The Paschen, Brackett and Pfund series lie in the infrared. The theory works for hydrogen and hydrogen-like ions such as He⁺ and Li²⁺, but not for atoms with many electrons.

The Nucleus and Binding Energy

The nucleus contains protons and neutrons, together called nucleons. They are held together by the nuclear force, which is very strong, attractive and acts only over very short distances. The mass of a nucleus is always less than the total mass of its separate nucleons. This difference is the mass defect. The equivalent energy, found using 1 u = 931 MeV, is the binding energy: the energy released when the nucleus forms, or the energy needed to break it into separate nucleons. The binding energy per nucleon is highest, about 8.8 MeV, near mass number 56 (iron), which is why those nuclei are the most stable.

Radioactivity

Radioactivity is the spontaneous decay of unstable nuclei. The number decaying per second is proportional to the number present, so $N = N_0 e^{-\lambda t}$, an exponential decrease. The half-life is $T_{1/2} = \frac{0.6931}{\lambda}$ and the mean life is $\tau = \frac{1}{\lambda}$. In alpha decay the atomic number falls by 2 and the mass number by 4. In beta-minus decay the atomic number rises by 1 and the mass number stays the same. Alpha and beta decay change the nucleus into a different element. Gamma decay only releases extra energy from an excited nucleus and does not change Z or A.

Nuclear Fission and Fusion

In fission, a heavy nucleus such as uranium-235 absorbs a neutron and splits into two middle-sized nuclei, releasing about 200 MeV and two or three neutrons. These neutrons can cause further fissions, giving a chain reaction, which is controlled in a nuclear reactor. In fusion, light nuclei such as hydrogen isotopes combine to form a heavier nucleus. Fusion needs extremely high temperatures and is the source of energy in the sun and stars. In both processes the products have higher binding energy per nucleon, and the small loss of mass appears as energy through $E = mc^2$.

Common mistakes to avoid

• Mixing up mass number and atomic number. Z counts protons only; A counts protons plus neutrons.
• Mixing up the Lyman and Balmer series. Lyman lines end at n = 1, Balmer lines end at n = 2.
• Leaving binding energy in joules when the question wants MeV. Use 1 u = 931 MeV directly on the mass defect.
• Getting alpha decay wrong. It lowers Z by 2 and A by 4, so check that charge and mass number balance on both sides.
• Treating radioactive decay as linear. After two half-lives, one quarter remains, not zero.

Test yourself on these with the practice test, then check the worked reasoning in the solved MCQs.

Frequently asked questions

What are cathode rays?

They are streams of fast-moving electrons given out by the cathode in a discharge tube at low pressure. They travel in straight lines, carry negative charge and are deflected by electric and magnetic fields. Their properties do not depend on the cathode material or the gas in the tube, which showed that electrons are present in all matter.

How did Millikan measure the charge of the electron?

He sprayed tiny oil drops between two charged plates. He first measured how fast a drop fell under gravity, then applied an electric field and adjusted it so the electric force balanced the drop's weight. The charge on every drop came out as a whole-number multiple of about 1.6 × 10⁻¹⁹ C, which he took as the charge of one electron.

Why was Rutherford's model unstable?

In Rutherford's model electrons move around the nucleus like planets around the sun. A charge moving in a circle is accelerating, and classical electromagnetic theory says it must keep radiating energy. The electron would then lose energy and spiral into the nucleus, so atoms could not be stable. Bohr's model removed this problem with non-radiating orbits.

What is Bohr's quantisation condition?

An electron can move only in orbits where its angular momentum is a whole-number multiple of h/2π, that is mvr = nh/2π. In these stationary orbits it does not radiate energy. This condition brought quantum ideas into the structure of the atom and explained why hydrogen gives sharp spectral lines.

What decides the stability of a nucleus?

The main measure is binding energy per nucleon, the average energy needed to remove a nucleon from the nucleus. The higher it is, the more stable the nucleus. It peaks at about 8.8 MeV near mass number 56, so iron and nearby nuclei are the most stable. Very light and very heavy nuclei have lower values.

What is the difference between fission and fusion?

In fission a heavy nucleus such as uranium-235 splits into two lighter nuclei, releasing energy and neutrons. In fusion two light nuclei join to form a heavier one, which needs extremely high temperatures like those in stars. Both release energy because the products have a higher binding energy per nucleon than the starting nuclei.