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,

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- Wien's law: λ_{max}=W/T where λ_{max}=peak emission wavelength, W=Wien's constant, 2.90*10^-3 K

__Step 1: Finding the star's temperature__

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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=**λ**_{max}/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/(4****π****r^2)** where r=distance from star to Earth

Re-arranging this, we get:

P=4**π***I*r^2

P=4**π**(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)*

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A=(2.10910^33)/(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 4**π**r^2, that is **π**d^2. Re-arranging this we get:

d=sqrt(A/**π**)

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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