The graph between the energy of photoelectrons E and the wavelength of incident light ` (lamda ) ` is

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Answer

To solve the question regarding the graph between the energy of photoelectrons \( E \) and the wavelength of incident light \( \lambda \), we will follow these steps:

### Step 1: Understand the Relationship
According to Planck's quantum theory, the energy \( E \) of a photon is directly proportional to its frequency \( \nu \):
\[ E \propto \nu \]
We can express frequency in terms of wavelength:
\[ \nu = \frac{c}{\lambda} \]
where \( c \) is the speed of light. Thus, we can rewrite the energy equation as:
\[ E = h \nu = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant.

### Step 2: Analyze the Equation
From the equation \( E = \frac{hc}{\lambda} \), we can see that:
- \( h \) and \( c \) are constants.
- This implies that energy \( E \) is inversely proportional to the wavelength \( \lambda \):
\[ E \propto \frac{1}{\lambda} \]

### Step 3: Determine the Graph Shape
Since \( E \) is inversely proportional to \( \lambda \), we can express this relationship as:
\[ E \cdot \lambda = hc \]
This indicates that the product of energy and wavelength is a constant, which is characteristic of a hyperbolic relationship.

### Step 4: Sketch the Graph
1. On the y-axis, plot the energy \( E \).
2. On the x-axis, plot the wavelength \( \lambda \).
3. As \( \lambda \) approaches zero, \( E \) approaches infinity. Conversely, as \( \lambda \) increases, \( E \) decreases.
4. The graph will be a hyperbola that approaches the axes but never touches them.

### Conclusion
The graph between the energy of photoelectrons \( E \) and the wavelength of incident light \( \lambda \) is a hyperbola.