Population 2

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Nick Walker

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Ready to use

6 years, 1 month ago

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Nick Walker 5 years, 11 months ago

Published this.

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Nick Walker 6 years, 1 month ago

Gave some feedback: Ready to use

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Nick Walker 6 years, 1 month ago

Created this as a copy of Population.

Name	Status	Author	Last Modified
Population	Ready to use	Nick Walker	18/03/2024 11:41
Population 2	Ready to use	Nick Walker	19/03/2024 14:50

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

temp	integer	198
Energy_mantissa	decimal	dec("4.45")
Energy_log	integer	-21
Frequency_log	decimal	dec("12")
Frequency_mantissa	decimal	dec("6.72")
int_step	decimal	dec("0.672")
int_step2	integer	13
A1	decimal	dec("-1.627839333150386271687091914153657604328e-2")
B1	number	100
NuNl	decimal	dec("1.963533703389237352982244602424106365275e-1")
NuNl_rounded	decimal	dec("0.196")
EfromNuNl	decimal	dec("-4.450000000000000358124653293084979771161e+2")
EfromNuNl_rounded	decimal	dec("-4.45492415019851923089422055675684281015e+2")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(100..350)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

198

→ Used by:

A1
EfromNuNl
EfromNuNl_rounded

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Calculate the energy difference, $\Delta$ E, between two states given that the relative populations of these states, $N_u/N_l$ ={NuNl_rounded} when the temperature, T, is {temp} K. The number of molecules in the upper state is $N_u$ and the number of molecules in the lower state is $N_l$ ;

${\Delta}E$ = Gap 0. $\times$ 10^{Gap 1.} J

Advice

a) This question requires use of the equation that relates the relative populations of states to the temperature and the energy difference between them;

$\frac{N_u}{N_l}=e^{\frac{-{\Delta}E}{kT}}$

${\rm ln}(\frac{N_u}{N_l})=\frac{-{\Delta}E}{kT}$

$kT{\rm ln}(\frac{N_u}{N_l})={-{\Delta}E}$

$-(1.38~\times~10^{-23}{\rm~J~K^{-1}}\times~\var{temp}~{\rm K}~\times~{\rm{ln}~}\var{NuNl_rounded})=\var{Energy_mantissa}\times10^\var{Energy_log}{\rm J}$

b) To convert the energy of a photon into a frequency;

$E=h\nu~$

$\frac{E}{h}=\nu=\frac{\var{Energy_mantissa}~\times~10^\var{Energy_log}~\rm J}{6.626~\times10^{-34}~\rm~J~s}=\var{Frequency_mantissa}\times10^{\var{Frequency_log}}~{\rm Hz}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Nick Walker 5 years, 11 months ago

Nick Walker 6 years, 1 month ago

Nick Walker 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Population 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Nick Walker 5 years, 11 months ago

Nick Walker 6 years, 1 month ago

Nick Walker 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`