What is the energy in joules of a single photon of wavelength `250 xx 10^(-9)m?`

Explanation

To find the energy of a single photon with a wavelength of \( 250 \times 10^{-9} \) meters, we can use the formula derived from Planck's theory:

### Step 1: Write down the formula for energy
The energy \( E \) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) Joule seconds),
- \( c \) is the speed of light (\( 3 \times 10^8 \) meters/second),
- \( \lambda \) is the wavelength of the photon.

### Step 2: Substitute the values into the formula
Given:
- \( \lambda = 250 \times 10^{-9} \) meters,
- \( h = 6.626 \times 10^{-34} \) Joule seconds,
- \( c = 3 \times 10^8 \) meters/second.

Substituting these values into the energy formula:
\[ E = \frac{(6.626 \times 10^{-34} \text{ J s}) \times (3 \times 10^8 \text{ m/s})}{250 \times 10^{-9} \text{ m}} \]

### Step 3: Calculate the numerator
Calculate the product of \( h \) and \( c \):
\[ 6.626 \times 10^{-34} \times 3 \times 10^8 = 1.9878 \times 10^{-25} \text{ J m} \]

### Step 4: Calculate the energy
Now, divide the result from the previous step by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25} \text{ J m}}{250 \times 10^{-9} \text{ m}} = \frac{1.9878 \times 10^{-25}}{2.5 \times 10^{-7}} = 7.9512 \times 10^{-19} \text{ J} \]

### Step 5: Final result
Thus, the energy of a single photon of wavelength \( 250 \times 10^{-9} \) meters is approximately:
\[ E \approx 7.95 \times 10^{-19} \text{ J} \]