1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Butoxors [25]
3 years ago
5

A light bulb of 200W emits 1.5μm.How many photons are emmited per second.​

Mathematics
1 answer:
Vinvika [58]3 years ago
3 0

Answer:

Step-by-step explanation:

An incandescent light bulb filament is approximated by a black body radiator, and in the case of a 60W bulb the filament temperature is around 2500˚C which is 2870˚K.

There are a couple of standard black body results that we can use. Firstly the total irradiance emitted per unit area of black body is equal to:

Ed=σT4

where σ=5.67×10−8 Wm−2K−4 is the Stephan-Boltzmann constant. For our bulb we get:

Ed=5.67×10−8⋅28704=3.85×106 Wm−2

As this is a 60W bulb then it has a total irradiance of 60W. Therefore the equivalent black body surface area is:

603.85×106=1.56×10−5 m2

which is 15.6mm2 of filament area.

Secondly we have that the total number of photons emitted per second per unit area of black body is equal to:[1]

Qd=σQT3

where σQ=1.52×1015 photons.sec−1m−2K−3. For our bulb this is:

Qd=1.52×1015⋅28703=3.59×1025 photons.sec−1m−2

Multiplying by the bulb’s equivalent black body surface area gives the result we require:

3.59×1025⋅1.56×10−5=5.6×1020 photons/sec

As a sanity check we know that these photons have a total energy of 60 joules per second, so the average energy per photon is:

605.6×1020=1.1×10−19 joules

A photon of wavelength λ has energy E=hcλ, and so the average energy corresponds with a photon of wavelength:

λ=hc1.1×10−19=1.9μm

Here’s a chart of the power distribution by wavelength, with the average photon wavelength shown as the dashed line, and visible wavelengths highlighted:

emember that there are a higher proportion of photons for the longer, lower energy wavelengths, so the average is weighted to the right.

We can also see from the original calculation that the general case is:

QdWEd=σQT3WσT4=2.68×1022WT photons/sec

for a bulb of wattage W watts and filament temperature T ˚K. So the photon emission rate is inversely proportional to the filament temperature. As a somewhat counter-intuitive example, a 60W halogen bulb with 3200˚K filament only emits photons at 90% of the rate of the standard 60W bulb, despite being visibly brighter.

The reason is that as the temperature increases then an increased proportion of shorter wavelength photos are emitted and therefore the average energy per photon increases, decreasing the number emitted per second. However at the same time an increased proportion of the photons are visible rather than infra-red, making the bulb appear brighter. Here’s the power distribution chart with the 60W halogen curve added for comparison:

You might be interested in
Factor the following polynomial completely. x²n - y²n
Alekssandra [29.7K]

Answer:

(n)*(x+y)(x-y)

Step-by-step explanation:

First of all, you take the n out, and then you use the formula of x²- y² and it will equal to (x+y)(x-y).

8 0
3 years ago
Read 2 more answers
31 cups are = to how many gallons ​
Pavel [41]

The answer is 1.9 gallons

6 0
3 years ago
Read 2 more answers
A car rental company’s standard charge includes an initial fee plus an additional fee for each mile driven. the standard charge
kaheart [24]

Answer:

C=0.55M+24.65

Step-by-step explanation:

0.40M+0.15M=0.55M

18.95+5.70=24.65

3 0
3 years ago
What is 7.5% written as a fraction in simplest form
weqwewe [10]
3\4 ! you simply convert 7.5% into a fraction. (move the decimal point to the right two times. This should give you 75. Remember to put 75 over 100.
EX: 75/100
Next you must find the greatest common fact of both numbers. In this case the number is 25.
25 goes into 75 3 times. So that is your numerator or the number on top.
25 goes into 100 4 times. This will be your denominator or the number on the bottom.
Your answer should be 3/4! Make sure to show your work! good luck!
4 0
3 years ago
Read 2 more answers
Parallelogram or not ?
Zielflug [23.3K]

Answer:

I think so

Step-by-step explanation:

here's here's the definition of a parallelogram

"a four-sided plane rectilinear figure with opposite sides parallel."

3 0
3 years ago
Other questions:
  • Which expression is equivalent to 24 Superscript one-third
    9·1 answer
  • Alex drew the triangles shown. What correctly describes the triangles
    15·1 answer
  • The 100th term of 70​, 110​, 150​, ... is .
    5·2 answers
  • If you can buy 1/3 of a box of chocolates for 6 dollars how much can you purchase for 4 dollars?
    13·1 answer
  • Helppppppp ....................................................
    11·1 answer
  • the function f is defined by f(x)=150/x-z where z is a constant. find z if the value of f at x=1/5 is equal to 250
    12·2 answers
  • A bank made a farmer a loan of 1400 at 17% for 3 years compounded annually. What is the compound interest?
    6·1 answer
  • Please help I don’t get this the teacher doesn’t help :(
    13·1 answer
  • Kiran collects data about the number of trees on school property and the average standardized test scores for those schools. Kir
    11·2 answers
  • Number 3 I need some help
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!