Find the power emitted (quantium mech)

[leonne]

Homework Statement

consider a blackbody at t=7000 what is the power emitted through a hole 1m between$\lambda$= 4000 and 4001 angstrom

Homework Equations

P($\lambda$) d$\lambda$=A(2$\pi$hc²/$\lambda$⁵(...)d$\lambda$

The Attempt at a Solution

my question is the math, I thought u had to make a integral on both sides and have it go from 4000 to 4001, but the solution does not do this. they just plug in 4000 for $\lambda$ and for d$\lambda$ they have 10^-10 Is both ways correct? I don't remember what i got when i did the integral
thanks

 

[susskind_leon]

Strictly speaking, your way is "more correct". They use the fact that the range for lambda is very small and the expression is not going to change a lot. This way, the integration turns into a multiplication.

 

[leonne]

ok thanks