Let's solve each part of the problem step-by-step.

1. Calculate the energy of the photon

The energy of a photon $E$ can be calculated using the equation: $E = h \cdot f$

Where:

• $h$ is Planck's constant ($4.14 \times 10^{-15}$ eV·s)
• $f$ is the frequency of the photon ($5.23 \times 10^{14}$ Hz)

Plugging in the values: $E = 4.14 \times 10^{-15} \text{ eV·s} \times 5.23 \times 10^{14} \text{ Hz}$ $E = 2.17 \text{ eV}$

2. Calculate the maximum kinetic energy of the ejected photoelectron

The maximum kinetic energy $K_{\text{max}}$ of the ejected photoelectron can be found using the photoelectric equation: $K_{\text{max}} = E - \phi$

Where:

• $E$ is the energy of the photon (2.17 eV from the previous calculation)
• $\phi$ is the work function of the material (1.75 eV)

Plugging in the values: $K_{\text{max}} = 2.17 \text{ eV} - 1.75 \text{ eV}$ $K_{\text{max}} = 0.42 \text{ eV}$

3. Calculate the threshold frequency for the material

The threshold frequency $f_0$ is the minimum frequency of light required to eject an electron from the material. It can be calculated using the work function $\phi$ and Planck's constant $h$: $f_0 = \frac{\phi}{h}$

Where:

• $\phi$ is the work function (1.75 eV)
• $h$ is Planck's constant ($4.14 \times 10^{-15}$ eV·s)

Plugging in the values: $f_0 = \frac{1.75 \text{ eV}}{4.14 \times 10^{-15} \text{ eV·s}}$ $f_0 \approx 4.23 \times 10^{14} \text{ Hz}$

Summary of Results

1. Energy of the photon: $2.17 \text{ eV}$
2. Maximum kinetic energy of the ejected photoelectron: $0.42 \text{ eV}$
3. Threshold frequency for the material: $4.23 \times 10^{14} \text{ Hz}$

Would you like more details or have any questions? Here are some related questions for further exploration:

1. How does the energy of the photon change with frequency?
2. What is the relationship between the work function and the threshold frequency?
3. How can the kinetic energy of photoelectrons be measured experimentally?
4. What happens to the kinetic energy of the photoelectrons if the frequency of the incoming photons is doubled?
5. How does the material's work function affect the ejection of photoelectrons?
6. What role does Planck's constant play in the photoelectric effect?
7. How can the photoelectric equation be derived from basic principles?
8. What other factors, besides frequency, can influence the energy of ejected photoelectrons?

Tip: Always ensure the units are consistent when using physical constants and equations to avoid calculation errors.