Question

# A gas absorbs a photon of $355\mathrm{nm}$ and emits it at two wavelengths. If one of the emissions is at $680\mathrm{nm}$, the other is at

A

$1035\mathrm{nm}$

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B

$325\mathrm{nm}$

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C

$743\mathrm{nm}$

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D

$518\mathrm{nm}$

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Solution

## The correct option is C $743\mathrm{nm}$Step 1: Given dataThe wavelength of the photon$=355\mathrm{nm}$The wavelength of one emission$=680\mathrm{nm}$Step 2: Calculating the other wavelengthAccording to the formula, Absorbed energy$=$emitted energy$⇒\frac{\mathrm{hc}}{\mathrm{\lambda }}=\frac{\mathrm{hc}}{{\mathrm{\lambda }}_{1}}+\frac{\mathrm{hc}}{{\mathrm{\lambda }}_{2}}$$⇒\frac{1}{\mathrm{\lambda }}=\frac{1}{{\mathrm{\lambda }}_{1}}+\frac{1}{{\mathrm{\lambda }}_{2}}$$⇒\frac{1}{355}=\frac{1}{680}+\frac{1}{{\mathrm{\lambda }}_{2}}$$⇒\frac{1}{{\mathrm{\lambda }}_{2}}=\frac{1}{355}-\frac{1}{680}$$⇒\frac{1}{{\mathrm{\lambda }}_{2}}=\frac{680-355}{355×680}$$⇒{\mathrm{\lambda }}_{2}=743\mathrm{nm}$Final answer: The other wavelength that photon emits$=743\mathrm{nm}$

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The text contains a physics problem involving the calculation of the wavelength of a photon emitted by a gas after absorbing a photon of a different wavelength. The problem is structured as a multiple-choice question with a detailed solution provided.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Question

# A gas absorbs a photon of $355\mathrm{nm}$ and emits it at two wavelengths. If one of the emissions is at $680\mathrm{nm}$, the other is at

A

$1035\mathrm{nm}$

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B

$325\mathrm{nm}$

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C

$743\mathrm{nm}$

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D

$518\mathrm{nm}$

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Solution

## The correct option is C $743\mathrm{nm}$Step 1: Given dataThe wavelength of the photon$=355\mathrm{nm}$The wavelength of one emission$=680\mathrm{nm}$Step 2: Calculating the other wavelengthAccording to the formula, Absorbed energy$=$emitted energy$⇒\frac{\mathrm{hc}}{\mathrm{\lambda }}=\frac{\mathrm{hc}}{{\mathrm{\lambda }}_{1}}+\frac{\mathrm{hc}}{{\mathrm{\lambda }}_{2}}$$⇒\frac{1}{\mathrm{\lambda }}=\frac{1}{{\mathrm{\lambda }}_{1}}+\frac{1}{{\mathrm{\lambda }}_{2}}$$⇒\frac{1}{355}=\frac{1}{680}+\frac{1}{{\mathrm{\lambda }}_{2}}$$⇒\frac{1}{{\mathrm{\lambda }}_{2}}=\frac{1}{355}-\frac{1}{680}$$⇒\frac{1}{{\mathrm{\lambda }}_{2}}=\frac{680-355}{355×680}$$⇒{\mathrm{\lambda }}_{2}=743\mathrm{nm}$Final answer: The other wavelength that photon emits$=743\mathrm{nm}$

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The text contains a physics problem involving the calculation of the wavelength of a photon emitted by a gas after absorbing a photon of a different wavelength. The problem is structured as a multiple-choice question with a detailed solution provided.

TYPE: SINGLE_QUESTION_WITH_ANSWER