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![**Problem Statement:**
A photon of wavelength \( \lambda \) has energy \( E \). If its wavelength were made 10 times higher, its final measure of energy would be
**Multiple-Choice Options:**
- (A) \( (E)^{1/10} \)
- (B) \( E^{10} \)
- (C) \( E \times 10^{-1} \)
- (D) \( (4E)^{10} \)
**Explanation:**
This question asks us how the energy of a photon changes when its wavelength increases by a factor of ten.
The energy \( E \) of a photon is inversely proportional to its wavelength \( \lambda \), according to the equation:
\[ E = \frac{h c}{\lambda} \]
where \( h \) is Planck's constant and \( c \) is the speed of light.
If the wavelength \( \lambda \) becomes 10 times larger (\( \lambda \rightarrow 10\lambda \)), the energy \( E \) changes as follows:
\[ E \rightarrow \frac{h c}{10\lambda} = \frac{1}{10} \times \frac{h c}{\lambda} = \frac{E}{10} \]
Therefore, the correct option is:
- (C) \( E \times 10^{-1} \)](https://content.bartleby.com/qna-images/question/8c939cff-bc46-4066-b22a-d4e55e2c89ab/481a3494-efa1-4ea5-b738-8e61fb908536/8qfavl_processed.png)
Transcribed Image Text:**Problem Statement:**
A photon of wavelength \( \lambda \) has energy \( E \). If its wavelength were made 10 times higher, its final measure of energy would be
**Multiple-Choice Options:**
- (A) \( (E)^{1/10} \)
- (B) \( E^{10} \)
- (C) \( E \times 10^{-1} \)
- (D) \( (4E)^{10} \)
**Explanation:**
This question asks us how the energy of a photon changes when its wavelength increases by a factor of ten.
The energy \( E \) of a photon is inversely proportional to its wavelength \( \lambda \), according to the equation:
\[ E = \frac{h c}{\lambda} \]
where \( h \) is Planck's constant and \( c \) is the speed of light.
If the wavelength \( \lambda \) becomes 10 times larger (\( \lambda \rightarrow 10\lambda \)), the energy \( E \) changes as follows:
\[ E \rightarrow \frac{h c}{10\lambda} = \frac{1}{10} \times \frac{h c}{\lambda} = \frac{E}{10} \]
Therefore, the correct option is:
- (C) \( E \times 10^{-1} \)
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