Continuous, Emission Line & Absorption Line Spectrum (OCR A Level Physics)

An absorption line at a wavelength of 588 nm is observed in the spectrum from a star.

Determine the difference between the energy levels for the atoms in the gas responsible for this absorption line. Give your answer in electron volts.     

Answer:

Step 1: List the known quantities

• Wavelength,  λ = 588 nm = 5.88 × 10^–7 m

• Planck’s constant, h = 6.63 × 10^–34 J s

• Speed of light, c = 3.00 × 10⁸ m s^–1

 Step 2: Identify the appropriate equation 

 ΔE = 

 Step 3: Substitute the known values and calculate ΔE

 ΔE =  = 3.38 × 10^–19 J

 Step 4: Convert from J to eV

 ΔE =  = 2.11 eV

Explain why:

a) Hot, dense sources produce continuous spectra

b) Hot, low pressure gases produce emission spectra

c) Hot, dense sources observed through cool, low pressure gases produce absorption spectra

Answer:

Part (a)

Hot, dense sources, such as the cores of stars, produce continuous spectra because:

• In a hot, dense material, the atoms or molecules are so close together that they interact with one another

• This leads to a spread of energy states that are not clearly defined

• Therefore, photons of all frequencies are emitted leading to an uninterrupted band of colour 

Part (b)

Hot, low pressure gases produce emission line spectra, because:

• Hot gases produce emission line spectra when photons are emitted due to the transition of electrons between discrete energy levels in atoms of the gas

• The line spectrum has certain, fixed frequencies related to the differences in energy between the various energy levels of the atoms of the gas

• In a low pressure gas, the atoms or molecules are not close together

• This means the energy levels of the gas atoms or molecules are clearly quantised and well-defined

• Therefore, only photons which correspond to the differences in energy between the energy levels of a bound electron are seen

Part (c)

Hot, dense sources observed through cold gases produce absorption spectra because: 

• Atoms of different elements in the cold gas absorb energy emitted from the hot source but only at particular energy values

• These particular energy values correspond to the differences in energy between the energy levels of a bound electron

• This means that particular frequencies of light are absorbed, creating black lines in the continuous emission spectrum

You will be required to identify the part of the electromagnetic spectrum to which an absorption or an emission line belongs. To help with this, make sure you are familiar with the wavelength values.

You should also be able to determine the colour by knowing the wavelength when the absorption or emission lines are in the visible range.