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Part 4
Part a
A photon is a quantum (or packet of energy) of electromagnetic radiation. It has no rest mass and travels at the speed of light, carrying an amount of energy proportional to its frequency.
Part b(i)· 2 steps
To show the energy of each photon
The energy of a photon is given by the formula .
Identify the given values and constants.
Wavelength $\lambda = 620 \text{ nm} = 620 \times 10^{-9} \text{ m}$. Planck's constant $h = 6.63 \times 10^{-34} \text{ J s}$. Speed of light $c = 3.0 \times 10^8 \text{ m s}^{-1}$.Substitute the values into the formula and calculate.
$$ E = \frac{(6.63 \times 10^{-34} \text{ J s}) \times (3.0 \times 10^8 \text{ m s}^{-1})}{620 \times 10^{-9} \text{ m}} $$ $$ E = \frac{1.989 \times 10^{-25}}{620 \times 10^{-9}} \text{ J} $$ $$ E \approx 3.208 \times 10^{-19} \text{ J} $$ $$ E \approx 3.2 \times 10^{-19} \text{ J} $$ The energy of each photon is indeed $\boxed{3.2 \times 10^{-19} \text{ J}}$.
Part b(ii)· 2 steps
To calculate the number of photons falling on the metal surface each second
Intensity is power per unit area, and power is energy per second.
Calculate the power of the beam.
Power $P = I \times A$. Intensity $I = 5.0 \times 10^2 \text{ W m}^{-2}$. Area $A = 1.2 \times 10^{-3} \text{ m}^2$. $$ P = (5.0 \times 10^2 \text{ W m}^{-2}) \times (1.2 \times 10^{-3} \text{ m}^2) $$ $$ P = 0.60 \text{ W} $$Calculate the number of photons per second.
The number of photons per second $N = \frac{P}{E}$. Energy per photon $E = 3.2 \times 10^{-19} \text{ J}$ (calculated in (i)). $$ N = \frac{0.60 \text{ J s}^{-1}}{3.2 \times 10^{-19} \text{ J/photon}} $$ $$ N \approx 1.875 \times 10^{18} \text{ photons s}^{-1} $$ The number of photons falling on the metal surface each second is approximately $\boxed{1.9 \times 10^{18} \text{ photons s}^{-1}}$.
Part b(iii)· 2 steps
To explain if electrons will be ejected
Convert the work function to Joules.
Work function $\phi = 2.4 \text{ eV}$. $1 \text{ eV} = 1.602 \times 10^{-19} \text{ J}$. $$ \phi = 2.4 \times (1.602 \times 10^{-19} \text{ J}) $$ $$ \phi \approx 3.845 \times 10^{-19} \text{ J} $$Compare the photon energy with the work function.
Photon energy $E = 3.2 \times 10^{-19} \text{ J}$. Work function $\phi \approx 3.845 \times 10^{-19} \text{ J}$. Since $E < \phi$ ($3.2 \times 10^{-19} \text{ J} < 3.845 \times 10^{-19} \text{ J}$), the energy of the incident photons is insufficient to overcome the work function of the metal. Conclusion: $\boxed{\text{No electrons will be ejected}}$ from the metal surface.
Part 5
Part c(i)
The diagram of electric field lines and the trajectory of electrons
Electrons, being negatively charged, are deflected towards the positive plate. In the figure, they are deflected upwards, which means the upper plate is positive and the lower plate is negative. Electric field lines go from the positive plate to the negative plate (i.e., downwards). The trajectory of the electrons is parabolic.
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