MYTUTOR SUBJECT ANSWERS

842 views

A given star has a peak emission wavelength of 60nm, lies 7.10*10^19m away and the intensity of its electromagnetic radiation reaching the Earth is 3.33*10^-8Wm^-2. Calculate the star's diameter

With a problem like this, the key is to split it down into component parts.

We will treat the star as a perfect emitter and radiator, something known as a black body. There will be two physical laws we need to use:

-Stefan-Boltzmann law: P=σAT^4 where P=power dissipated by a black body, σ=Stefan-Boltzmann constant, 5.67*10^-8 W*(m^-2)*(K^-4), A=surface area of the body, T=temperature

-Wien's law: λmax=W/T where λmax=peak emission wavelength, W=Wien's constant, 2.90*10^-3 K*m, T=temperature

Step 1: Finding the star's temperature

The peak emission wavelength of the star is given in the question as 60nm, which is 6.0*10^-8 m in standard form. Re-arranging the formula for Wien's law we get:

T=λmax/W

T=(6.0*10^-8)/(2.90*10^-3)

T=48330 K 4.s.f

Step 2: Finding the power of the star

In order for us to use the Stefan-Boltzmann law, we need the power emitted by the star. Currently we have the intensity at the Earth's surface. Light propagates out spherically so the intensity is given by:

I=P/(4πr^2) where r=distance from star to Earth

Re-arranging this, we get:

P=4π*I*r^2

P=4π(3.33*10^-8)(7.10*10^19)^2

P=2.109*10^33 W 4.s.f

Step 3: Finding the surface area of the star

Re-arranging the Stefan-Boltzmann law we get:

A=P/(σ*T^4)

A=(2.109*10^33)/(5.67*10^-8)(48330)^4

A=6.818*10^21 m^2 4.s.f

Step 4: Finding the diameter of the star

As the star is spherical, it's area is 4πr^2, that is πd^2. Re-arranging this we get:

d=sqrt(A/π)

d=sqrt(6.818*10^21/π)

Diameter= 4.66*10^10 m 3.s.f

Note on significant figures: By making sure to keep to 4.s.f at each stage of the calculation, you ensure that the final answer will be correct to 3.s.f

James S. A Level Maths tutor, A Level Physics tutor, A Level Further ...

2 years ago

Answered by James, an A Level Physics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

116 SUBJECT SPECIALISTS

£26 /hr

Daniel K.

Degree: Mathematical and Theoretical Physics (Masters) - Oxford, Merton College University

Subjects offered:Physics, Science+ 5 more

Physics
Science
Maths
Further Mathematics
Chemistry
.MAT.
-Personal Statements-

“Mathematics and Theoretical Physics, University of Oxford. I enjoy sharing my experience and enthusiasm in Maths with those who could do with some help”

PremiumJacan C. A Level Maths tutor, A Level Physics tutor, GCSE Physics tut...
£36 /hr

Jacan C.

Degree: Theoretical Physics (Masters) - York University

Subjects offered:Physics, Science+ 3 more

Physics
Science
Maths
Further Mathematics
Chemistry

“Helping the striving and the struggling with caring, friendly and structured tuition. With 200+ hours of experience, offering Physics, Maths and Chemistry.”

£30 /hr

Anuradha D.

Degree: Physics (Masters) - Durham University

Subjects offered:Physics, Music+ 4 more

Physics
Music
Maths
Further Mathematics
Chemistry
-Personal Statements-

“Hello everyone! My name is Anuradha (you can call me Anu), and I am a Physics Undergrad at Durham. I have always had a “thing” for science and am so pleased to be studying it – and hope that I can give you all the support you need to ...”

About the author

£20 /hr

James S.

Degree: Mathematics and Physics (MSci) (Masters) - Durham University

Subjects offered:Physics, Maths+ 1 more

Physics
Maths
Further Mathematics

“First year Maths and Physics undergraduate at Durham University. Previous tutoring experience with A-level students”

MyTutor guarantee

You may also like...

Posts by James

A given star has a peak emission wavelength of 60nm, lies 7.10*10^19m away and the intensity of its electromagnetic radiation reaching the Earth is 3.33*10^-8Wm^-2. Calculate the star's diameter

Find the stationary point of y=3x^2-12x+29 and classify it as a maximum/minimum

Using mathematical induction, prove that n^3+2n is divisible by 3 for all integers n

Other A Level Physics questions

What is an equipotential in an electric/gravitational field?

Describe and explain the photoelectric effect (6 marks)

A roller coaster has a loop, r = 20m, how fast should it travel so that riders don't fall out?

What is the definition of the photoelectric effect?

View A Level Physics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok