Calculate the energy in joule corresponding to light of wavelength 45 nm (Planck.s constant `h=6.63xx10^(-34)` Js, speed of light `c=3xx10^(8) ms^(-1))`

Options

A. `6.67xx10^(12)`
B. `4.42xx10^(-13)`
C. `4.42xx10^(-18)`
D. `6.67xx10^(12)`

Explanation

To calculate the energy corresponding to light of wavelength 45 nm, we can use the formula that relates energy (E) to wavelength (λ) and the speed of light (c). The relationship is given by:

\[ E = \frac{hc}{\lambda} \]

Where:
- \( E \) is the energy in joules,
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \) Js),
- \( c \) is the speed of light (\( 3 \times 10^{8} \) m/s),
- \( \lambda \) is the wavelength in meters.

### Step 1: Convert the wavelength from nanometers to meters
Given that \( 1 \text{ nm} = 10^{-9} \text{ m} \), we convert 45 nm to meters:

\[ \lambda = 45 \text{ nm} = 45 \times 10^{-9} \text{ m} \]

### Step 2: Substitute the values into the energy formula
Now, we can substitute the values of \( h \), \( c \), and \( \lambda \) into the energy formula:

\[ E = \frac{(6.63 \times 10^{-34} \text{ Js}) \times (3 \times 10^{8} \text{ m/s})}{45 \times 10^{-9} \text{ m}} \]

### Step 3: Calculate the numerator
First, calculate the numerator:

\[ 6.63 \times 10^{-34} \text{ Js} \times 3 \times 10^{8} \text{ m/s} = 1.989 \times 10^{-25} \text{ Jm} \]

### Step 4: Calculate the energy
Now, divide the result from the numerator by the wavelength in meters:

\[ E = \frac{1.989 \times 10^{-25} \text{ Jm}}{45 \times 10^{-9} \text{ m}} \]

Calculating this gives:

\[ E = \frac{1.989 \times 10^{-25}}{45 \times 10^{-9}} \approx 4.42 \times 10^{-18} \text{ J} \]

### Final Answer
Thus, the energy corresponding to light of wavelength 45 nm is approximately:

\[ E \approx 4.42 \times 10^{-18} \text{ J} \]

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