Use the graph below to answer the following question:

Graph titled maximum kinetic energy of ejected photo electron versus incoming frequency is shown. The y axis is labeled maximum kinetic energy and scales from negative 3 to positive 3 electron volts. The x axis is labeled frequency from 0 to 11 times 10 to the 14 hertz. A line connects the points 0, negative 2 and 2.5, negative 1 and 5, 0 and 8, 1 and 10, 2.

If the incoming photon had a frequency of 8.0 E14 Hz, would you have a photo-electron ejected?

Yes
No
Only 50% of the time
Not enough information

To determine whether a photo-electron would be ejected, we need to analyze the graph that relates the maximum kinetic energy of ejected photo-electrons to the incoming frequency of photons. 

Given:
- The graph shows the kinetic energy \( K \) versus frequency \( f \).
- The x-axis (frequency) ranges from 0 to \( 11 \times 10^{14} \) Hz.
- The y-axis (maximum kinetic energy) ranges from -3 to 3 electron volts (eV).

Key points on the line in the graph:
- (0, -2)
- (2.5, -1)
- (5, 0)
- (8, 1)
- (10, 2)

From the graph, we observe that:
- At frequency \( f = 5 \times 10^{14} \) Hz, the kinetic energy \( K = 0 \) eV. This frequency is known as the threshold frequency \( f_0 \). 
- For frequencies greater than \( f_0 \), the kinetic energy \( K \) becomes positive, indicating that photo-electrons are ejected.
- For frequencies less than \( f_0 \), the kinetic energy \( K \) is negative or zero, indicating no ejection of photo-electrons.

Given frequency:
- The incoming photon has a frequency of \( 8.0 \times 10^{14} \) Hz.

From the graph, at \( f = 8.0 \times 10^{14} \) Hz:
- The kinetic energy \( K = 1 \) eV.

Since the kinetic energy is positive (1 eV), a photo-electron will indeed be ejected.

So, the answer is:

**Yes**

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

1. What is the relationship between the kinetic energy of an ejected photo-electron and the frequency of the incoming photon?
2. How do you determine the threshold frequency from a graph of kinetic energy versus frequency?
3. What happens to the kinetic energy if the frequency of the incoming photon is just below the threshold frequency?
4. How can you calculate the work function from the given graph?
5. What is the significance of the slope of the line in the kinetic energy versus frequency graph?
6. How does the photoelectric effect support the particle nature of light?
7. What is the equation relating kinetic energy, photon energy, and work function?
8. What factors can affect the ejection of photo-electrons apart from the frequency of incoming photons?

**Tip:** Always look for the threshold frequency (where kinetic energy is zero) to determine if photo-electrons will be ejected for a given photon frequency.

Explore the relationship between photon frequency and maximum kinetic energy in the photoelectric effect. Analyze a graph and determine if a photo-electron is ejected at a given frequency of 8.0 E14 Hz. Key concepts include the threshold frequency and Einstein's Photoelectric Equation.

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