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\pihc²/\lambda⁵(...)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