Dual Nature of Radiation and Matter: One Mark Questions, Book Back Answers and Notes

About Dual Nature of Radiation and Matter

Medium ~120 min study

In the last unit, interference and diffraction showed that light is a wave. This unit shows the other side. When light falls on a metal and knocks out electrons, the results make sense only if light arrives as separate packets of energy called photons. Classical wave theory could not explain these results, and that failure opened the way to quantum physics.

The unit moves in two steps. First it shows the particle nature of radiation, through electron emission and the photoelectric effect explained by Einstein. Then it turns the idea around: de Broglie proposed that moving particles have waves associated with them, and the Davisson-Germer experiment confirmed this by diffracting electrons from a crystal.

Numericals on Einstein's photoelectric equation and on de Broglie wavelength are common, along with short answers on the laws of photoelectric emission. The same ideas come back in atomic and nuclear physics, and they explain how an electron microscope can see far finer detail than an ordinary microscope.

What you'll learn

• Describe the different types of electron emission from metal surfaces.
• State and explain the laws of photoelectric emission from experimental results.
• Calculate photon energy, work function and maximum kinetic energy using Einstein's equation.
• Derive the de Broglie wavelength of a particle and of an electron accelerated through a potential difference.
• Explain the construction, working and uses of a photo-emissive cell.
• Explain how X-rays are produced and describe their continuous and characteristic spectra.

Before you start

• Wave nature of light from wave optics
• Basic structure of the atom
• Law of conservation of energy
• Kinetic energy and the energy gained by a charge in a potential difference (eV)

Dual Nature of Radiation and Matter explained

Wave-Particle Duality, Step by Step

Electron Emission and the Photoelectric Effect

Electrons in a metal need a minimum energy, the work function, to escape. They can get it from heat (thermionic emission), a strong electric field (field emission), light (photoelectric emission) or fast electrons striking the surface (secondary emission). Hallwachs and Lenard studied photoelectric emission and found results that wave theory could not explain. The photocurrent depends on the intensity of light, but the maximum kinetic energy of the emitted electrons depends only on the frequency of the light and the metal, not on intensity. Below a threshold frequency no electrons come out, however bright the light. Emission is also instantaneous.

Einstein's Photoelectric Equation

Einstein proposed that light consists of photons, each with energy $E = h\nu$. One photon gives all its energy to one electron. Part of it is used to overcome the work function $\phi_0$ and the rest appears as kinetic energy: $h\nu = \phi_0 + \frac{1}{2}mv_{max}^2$. Since the maximum kinetic energy equals $eV_0$, a graph of stopping potential against frequency is a straight line with slope h/e. This explained every law of photoelectric emission and gave strong evidence for the particle nature of light.

Photocells and Their Uses

A photocell converts light energy into electrical energy. Photocells are of three types: photo-emissive, photo-voltaic and photo-conductive. The textbook describes the photo-emissive cell, in which light falling on a cathode releases electrons that are collected by an anode. Photocells are used in automatic street lights, burglar alarms, exposure meters in photography and the reproduction of sound in motion pictures.

de Broglie's Matter Waves

Louis de Broglie argued that if light can behave like particles, particles should also behave like waves. A particle of momentum p has a wavelength $\lambda = \frac{h}{p} = \frac{h}{mv}$. For an electron accelerated through a potential difference V, this becomes $\lambda = \frac{12.27}{\sqrt{V}}$ Å. At 100 V that is about 1.227 Å, close to the spacing of atoms in a crystal. Every moving body has such a wave, but for everyday objects the wavelength is far too small to detect.

Davisson-Germer Experiment and the Electron Microscope

Davisson and Germer fired electrons accelerated through 54 V at a nickel crystal and found a strong diffracted beam at 50°. The wavelength worked out from this matched de Broglie's value of about 1.67 Å, confirming that electrons behave as waves. The electron microscope uses this idea. Fast electrons have wavelengths much shorter than visible light, so it can resolve far smaller details than an optical microscope.

X-Rays

X-rays are produced when fast electrons strike a metal target in a Coolidge tube. Electrons slowing down in the target give a continuous spectrum, which has a sharp lower limit of wavelength, $\lambda_0 = \frac{hc}{eV}$. Electrons jumping between inner shells of target atoms give sharp characteristic lines that depend on the target material. X-rays are used in medical diagnosis, detecting cracks in metal parts and studying crystal structure.

Common mistakes to avoid

• Mixing up intensity and frequency. Intensity decides the photocurrent; frequency decides the maximum kinetic energy.
• Trying to explain threshold frequency with wave theory. Only the photon picture explains why bright red light may eject no electrons while dim violet light does.
• Unit errors in de Broglie wavelength. Convert mass to kg, energy to joules and use h = 6.626 × 10⁻³⁴ J s.
• Forgetting the work function. Maximum kinetic energy is hν minus φ₀, not the full photon energy.
• Swapping the two X-ray spectra. The continuous spectrum comes from electrons slowing down; characteristic lines come from inner-shell transitions in target atoms.

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

Frequently asked questions

What is threshold frequency in the photoelectric effect?

It is the minimum frequency of light that can eject electrons from a given metal. Below this frequency no electrons are emitted, no matter how intense the light is. It depends on the work function: ν₀ = φ₀/h.

How does light intensity affect the photoelectric current?

As long as the frequency is above threshold, the photocurrent is directly proportional to intensity. Higher intensity means more photons strike the surface each second, so more electrons are emitted. Intensity does not change their maximum kinetic energy.

What did the Davisson-Germer experiment prove?

Electrons accelerated through 54 V were diffracted by a nickel crystal, giving a peak at 50°. Diffraction is a wave property, and the measured wavelength agreed with de Broglie's formula. This was experimental proof of the wave nature of matter.

Why can we not see the wave nature of a moving car?

The de Broglie wavelength is h/mv. A car has a very large mass, so its wavelength is extremely small, far below anything that can be measured. Wave effects are noticeable only for very light particles such as electrons.

How is a photon different from an ordinary particle?

A photon has zero rest mass and always travels at the speed of light in vacuum. Its energy depends only on its frequency, E = hν, and its momentum is h/λ. An ordinary particle has rest mass and can move at any speed less than that of light.

How are X-rays produced in a Coolidge tube?

A heated filament emits electrons, which are accelerated by a high voltage towards a metal target. When they strike the target, a small fraction of their kinetic energy is converted into X-rays. Most of the energy becomes heat, so the target is made of a metal with a high melting point, such as tungsten, and is cooled.