text: 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
  
  $1035\mathrm{nm}$
  
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  B
  
  $325\mathrm{nm}$
  
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  C
  
  $743\mathrm{nm}$
  
  Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
  D
  
  $518\mathrm{nm}$
  
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  Open in App
  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}$
  
  Suggest Corrections
  0
  Explore more
explanation: The document contains a physics question related to the absorption and emission of photons by a gas. It provides a multiple-choice question with options and a detailed solution. The correct answer is given as option C, which is \(743\mathrm{nm}\).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 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
  
  $1035\mathrm{nm}$
  
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  B
  
  $325\mathrm{nm}$
  
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  C
  
  $743\mathrm{nm}$
  
  Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
  D
  
  $518\mathrm{nm}$
  
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  Open in App
  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}$
  
  Suggest Corrections
  0
  Explore more
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a physics question related to the absorption and emission of photons by a gas. It provides a multiple-choice question with options and a detailed solution. The correct answer is given as option C, which is \(743\mathrm{nm}\).
  
  Label: question-and-answer