Calculate the energy in joule corresponding to light of wavelength 45 nm : `("Planck's constant "h=6.63 xx 10^(-34)" Js: speed of light :"c =3 xx 10^8 "ms"^(-1))`.

Options

A. `6.67xx10^(15)`
B. `6.67xx10^(11)`
C. `4.42 xx10^(-15)`
D. `4.42 xx10^(-18)`

Answer

To calculate the energy corresponding to light of wavelength 45 nm, we can use the formula derived from Planck's theory:

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

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-by-Step Solution:

**Step 1: Convert the wavelength from nanometers to meters.**
- Given wavelength \( \lambda = 45 \) nm.
- Convert nanometers to meters:
\[ \lambda = 45 \, \text{nm} = 45 \times 10^{-9} \, \text{m} \]

**Step 2: Substitute the values into the energy formula.**
- Using the formula \( E = \frac{hc}{\lambda} \):
\[ E = \frac{(6.63 \times 10^{-34} \, \text{Js}) \times (3 \times 10^8 \, \text{m/s})}{45 \times 10^{-9} \, \text{m}} \]

**Step 3: Calculate the numerator.**
- Calculate \( h \times c \):
\[ h \times c = 6.63 \times 10^{-34} \times 3 \times 10^8 = 1.989 \times 10^{-25} \, \text{Js m} \]

**Step 4: Divide by the wavelength.**
- Now divide by \( \lambda \):
\[ E = \frac{1.989 \times 10^{-25}}{45 \times 10^{-9}} = \frac{1.989 \times 10^{-25}}{4.5 \times 10^{-8}} = 4.42 \times 10^{-18} \, \text{J} \]

**Step 5: Final result.**
- The energy corresponding to light of wavelength 45 nm is:
\[ E \approx 4.42 \times 10^{-18} \, \text{J} \]

### Conclusion:
The correct answer is \( 4.42 \times 10^{-18} \, \text{J} \).