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, 5.6710^-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, 2.9010^-3 Km, 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 6.010^-8 m in standard form. Re-arranging the formula for Wien's law we get:

T=λmax/W

T=(6.010^-8)/(2.9010^-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=4πIr^2

P=4π(3.3310^-8)(7.1010^19)^2

P=2.10910^33 W 4.s.f

Step 3: Finding the surface area of the star

Re-arranging the Stefan-Boltzmann law we get:

A=P/(σT^4)

A=(2.10910^33)/(5.6710^-8)(48330)^4

A=6.81810^21 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(6.81810^21/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

Answered by James S. Physics tutor

3770 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

In the Rutherford alpha scattering experiment, most particles passed straight through the foil with little or no deflection. What can be deduced about the structure of the atom from this?


A 100g mass is on a circular turntable spinning at 78 revolutions per minute. The maximum frictional force between the mass and turntable is 0.50N. Find the maximum distance from the center of the turntable at which the mass would stay on the turntable.


Two balls of mass 3kg and 7 kg respectively move towards one another with speeds 5ms^-1 and 2ms^-1 respectively on a smooth table. If they collide and join, what velocity do they move off with?


Give examples of how the photoelectric effect supports the particle nature of light and defies the wave theory.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences