Dual Nature of Radiation and Matter

Flashcards covering the dual nature of radiation and matter, properties of photons, quantum theory, the photoelectric effect, and de-Broglie matter waves.

What phenomena of light are explained by assuming light is a wave, and which are explained by assuming it is a particle?

Interference, diffraction, and polarization are explained as waves, while the photoelectric effect is explained as a particle.

What is the speed ($c$) and rest mass of a photon in a vacuum?

The speed is $c = 3 \times 10^8 \, \text{m/sec}$ and the rest mass is zero.

What are the formulas for the energy ($E$) and momentum ($P$) of a photon?

$E = hv = \frac{hc}{\lambda}$ and $P = \frac{E}{c} = \frac{hv}{c} = \frac{h}{\lambda}$.

How does increasing the intensity of light of a given frequency affect photons?

It increases the number of photons per unit area per unit time, but the energy of each photon remains the same.

What is the formula to calculate the energy of a photon in electron volts ($eV$) when the wavelength is given in Angstroms ($A$)?

$E \, \text{in (eV)} = \frac{12375}{\lambda(A)}$ or $\frac{12400}{\lambda(A)}$.

What is the 'kinetic mass' or 'effective mass' of a photon?

$m = \frac{E}{c^2} = \frac{hv}{c^2} = \frac{h}{c\lambda}$.

Define 'Work Function' ($\phi$).

The minimum energy of incident radiation required to eject electrons from a metallic surface.

What happens if the incident frequency ($v$) is less than the threshold frequency ($v_0$)?

No photoelectron emission occurs.

In which region of the spectrum is the threshold frequency for potassium and caesium oxides?

In the visible spectrum, specifically with a wavelength ($\lambda$) between $400$ and $700 \, \text{nm}$.

What is the maximum wavelength of incident radiation required to eject electrons called?

Threshold wavelength ($\lambda_0$).

Identify the three types of electron emission described in the notes.

1. Thermionic emission (heat energy), 2. Photo-electric emission (light), 3. Field emission (high electric field).

What magnitude of electric field is required for 'field emission' or 'cold emission'?

An electric field of the order of $10^8 \, \text{Vm}^{-1}$.

According to Einstein, what is the nature of the collision in the photoelectric effect?

A one-to-one inelastic collision between a photon and an electron in which the photon is completely absorbed.

What is Einstein's photoelectric equation?

$E = \phi + K_{max}$, where $K_{max} = \frac{1}{2}mv_{max}^2$ is the maximum kinetic energy of emitted electrons.

Define 'stopping potential' ($V_0$).

The minimum negative potential applied to plate A for which the photoelectric current becomes zero.

How are the maximum kinetic energy ($K_{max}$) and the stopping potential ($V_0$) related?

$K_{max} = eV_0$.

How does the intensity of incident light affect the stopping potential and saturation current?

Intensity does not affect the stopping potential, but it increases the saturation current.

In a graph of stopping potential ($V_0$) versus frequency ($v$), what do the slope and intercept represent?

The slope is $\frac{h}{e}$ and the intercept is $\frac{hv_0}{e}$.

What is the typical time lag for photoelectric emission?

$10^{-9} \, \text{s}$ or less.

What are the two parts the energy ($hv$) of an incident photon is used for according to Einstein's theory?

Part (a) to liberate the electron (equal to work function $\phi_0$) and Part (b) to impart kinetic energy to the ejected electron.

How is 'quantum efficiency' defined in the context of the photoelectric effect?

$\eta = \frac{\text{no. of electrons ejected/sec}}{\text{no. of photons incident/sec}} \times 100\%$.

What is the formula for the de-Broglie wavelength ($\lambda$)?

$\lambda = \frac{h}{p} = \frac{h}{mv} = \frac{h}{\sqrt{2mE}}$, where $E$ is kinetic energy.

What are two distinct characteristics of matter waves?

They are not electromagnetic and they are independent of the charge on the material particle.

How many de-Broglie waves are associated with the $n^{th}$ orbital electron?

The number is $n$.

What is the kinetic energy ($KE$) of an electron following a circular path of radius ($R$) in a magnetic field ($B$)?

$KE = \frac{e^2 B^2 R^2}{2m}$.