Which curve shows the relation ship between the energy R and the wavelength `lamda` of a photon of electromagnetic radiation?

Options

A.
B.
C.
D.

Explanation

To solve the problem of determining which curve shows the relationship between the energy \( E \) and the wavelength \( \lambda \) of a photon of electromagnetic radiation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship**: The energy \( E \) of a photon is given by the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant and \( c \) is the speed of light.

2. **Rearranging the equation**: From the equation, we can see that energy \( E \) is inversely proportional to the wavelength \( \lambda \):
\[ E \propto \frac{1}{\lambda} \]

3. **Identifying the relationship**: Since \( E \) is inversely proportional to \( \lambda \), we can express this relationship in a more mathematical form:
\[ E = k \cdot \frac{1}{\lambda} \]
where \( k = hc \) is a constant.

4. **Graphical representation**: The equation \( E = \frac{k}{\lambda} \) indicates that if we plot \( E \) against \( \lambda \), we will get a hyperbolic curve. This is because as \( \lambda \) increases, \( E \) decreases, and vice versa.

5. **Analyzing the options**: When looking at the provided options for graphs, we need to identify which one represents a hyperbola. A hyperbola in the \( xy \) plane can be represented as \( xy = k \), which is consistent with our derived relationship.

6. **Conclusion**: After analyzing the graphs, we find that the curve that represents the relationship between energy \( E \) and wavelength \( \lambda \) is the hyperbolic curve. Therefore, the correct option is the one that shows a hyperbola.

### Final Answer:
The curve that shows the relationship between the energy \( E \) and the wavelength \( \lambda \) of a photon of electromagnetic radiation is a hyperbola.

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