In a series of photoelectric emission experiments on a certain metal surface, possible relationships between the following quantities were investigated: threshold frequency `f_0`, frequency of incident light f, light intensity P, photocurrent I, maximum kinetic energy of photoelectrons `T_(max)`. Two of these quantities, when plotted as a graph of y against x, give a straight line through the origin. Which of the following correctly identifies x and y with the photoelectric quantities ?

Options

A. x I y `f_0`
B. x f y `f_0`
C. x P y I
D. x P y `T_(max)`

Explanation

To solve the problem, we need to identify which two quantities among the given options give a straight line through the origin when plotted against each other. The quantities we are considering are:

1. Threshold frequency \( f_0 \)
2. Frequency of incident light \( f \)
3. Light intensity \( P \)
4. Photocurrent \( I \)
5. Maximum kinetic energy of photoelectrons \( T_{max} \)

### Step-by-Step Solution:

**Step 1: Understand the relationship between the quantities.**
- The photoelectric effect is described by Einstein's photoelectric equation:
\[ T_{max} = hf - \phi \]
where \( h \) is Planck's constant and \( \phi \) is the work function of the metal. This equation shows that \( T_{max} \) is linearly related to the frequency \( f \) but does not pass through the origin because when \( f = f_0 \) (the threshold frequency), \( T_{max} = 0 \).

**Step 2: Analyze the relationship between intensity and photocurrent.**
- The intensity \( P \) of light is proportional to the number of photons striking the metal surface per unit time. The photocurrent \( I \) is directly proportional to the number of photoelectrons emitted, which in turn is proportional to the number of incident photons (assuming each photon can release one electron).
- Therefore, we have the relationship:
\[ I \propto P \]
This means that if the intensity \( P \) is zero, the photocurrent \( I \) will also be zero, indicating that this relationship passes through the origin.

**Step 3: Determine the correct quantities for the graph.**
- Since we have established that \( I \) is directly proportional to \( P \) and passes through the origin, we can conclude that:
- Let \( x = P \) (light intensity)
- Let \( y = I \) (photocurrent)

### Conclusion:
The correct identification of \( x \) and \( y \) is:
- \( x = P \)
- \( y = I \)

This means that when we plot photocurrent \( I \) against light intensity \( P \), we get a straight line through the origin.