The energy of a photon of wavelength `lambda` is

Options

A. `hclambda`
B. `(hc)/(lambda)`
C. `(lambda)/(hc)`
D. `lambdah/c`

Answer

To find the energy of a photon with a wavelength \( \lambda \), we can follow these steps:

### Step 1: Understand the relationship between energy and frequency
The energy \( E \) of a photon is directly proportional to its frequency \( \nu \). This relationship is given by the equation:
\[ E = h \nu \]
where \( h \) is Planck's constant.

### Step 2: Relate frequency to wavelength
We know the relationship between the speed of light \( c \), frequency \( \nu \), and wavelength \( \lambda \) is given by:
\[ c = \nu \lambda \]
From this equation, we can express frequency \( \nu \) in terms of wavelength \( \lambda \):
\[ \nu = \frac{c}{\lambda} \]

### Step 3: Substitute frequency into the energy equation
Now, we can substitute the expression for frequency \( \nu \) into the energy equation:
\[ E = h \nu = h \left(\frac{c}{\lambda}\right) \]

### Step 4: Simplify the equation
This simplifies to:
\[ E = \frac{hc}{\lambda} \]
This equation gives us the energy of a photon in terms of its wavelength \( \lambda \).

### Final Answer
Thus, the energy of a photon of wavelength \( \lambda \) is:
\[ E = \frac{hc}{\lambda} \]

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