The energy of a photon is `3 xx10^(-12)erg`.What is its wavelength in nm?`(h=6.62xx10^(-27)erg-s,3xx10^(10)cm s^(-1))`

Options

A. 662
B. 1324
C. 66.2
D. 6.62

Answer

To find the wavelength of a photon given its energy, we can use the formula that relates energy (E), Planck's constant (h), and the speed of light (c) to wavelength (λ):

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

From this formula, we can rearrange it to solve for wavelength (λ):

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Energy of the photon (E) = \( 3 \times 10^{-12} \) erg
- Planck's constant (h) = \( 6.62 \times 10^{-27} \) erg·s
- Speed of light (c) = \( 3 \times 10^{10} \) cm/s

2. **Substitute the values into the wavelength formula:**
\[ \lambda = \frac{(6.62 \times 10^{-27} \text{ erg·s}) \times (3 \times 10^{10} \text{ cm/s})}{3 \times 10^{-12} \text{ erg}} \]

3. **Calculate the numerator:**
\[ (6.62 \times 10^{-27}) \times (3 \times 10^{10}) = 19.86 \times 10^{-17} \text{ erg·cm} \]

4. **Now divide by the energy:**
\[ \lambda = \frac{19.86 \times 10^{-17} \text{ erg·cm}}{3 \times 10^{-12} \text{ erg}} = \frac{19.86}{3} \times 10^{-17 + 12} \text{ cm} \]

5. **Perform the division:**
\[ \frac{19.86}{3} \approx 6.62 \]

6. **Combine the powers of ten:**
\[ \lambda = 6.62 \times 10^{-5} \text{ cm} \]

7. **Convert cm to nm:**
- We know that \( 1 \text{ cm} = 10^7 \text{ nm} \), so:
\[ \lambda = 6.62 \times 10^{-5} \text{ cm} \times 10^7 \text{ nm/cm} = 6.62 \times 10^2 \text{ nm} = 662 \text{ nm} \]

### Final Answer:
The wavelength of the photon is **662 nm**.