The determination of frequency v from Planck's formula

[redbaldyhead]

Homework Statement

B=10^-7Wm^-2Hz^-1sr^-1;T=10^4K
h=6.6x10^-34J.s
k=1.4x10-23JK^-1
c=3.0x10^8m^-1

Homework Equations

Calculate v fom Bv(T)=(2hv^3)/(c^2)x1/(exp(hv/kT)-1)

The Attempt at a Solution

I have managed to obtain a LHS= (Bc^2/2h)xexp(h/kT)
but RHS is posing a problem to me!
I just cannot resolve v^3/(exp v-1)
I have tried the tactic of changing the base of the exp to log10 throughout but I am still left with v^3/((log v/log 2.718) - .4342) on the RHS to deal with!
I should expect an answer v = 10^15 Hz but the best I get is ~10^18

Thanks I hope I have made this clear as I'm not particularly computer literate

 

[Jhero]

Thank you for your post. You have made good progress in solving this problem. To obtain the correct answer of v= 10^15 Hz, you need to rearrange the equation to isolate v on one side. Here is a step-by-step solution:

1. Begin with the equation: Bv(T) = (2hv^3)/(c^2)x1/(exp(hv/kT)-1)

2. Substitute in the given values for B, h, c, and k: B=10^-7Wm^-2Hz^-1sr^-1;T=10^4K; h=6.6x10^-34J.s; k=1.4x10-23JK^-1; c=3.0x10^8m^-1

3. Rearrange the equation to isolate v: v^3 = (Bc^2/2h)x1/(exp(hv/kT)-1)

4. Take the cube root of both sides: v = (Bc^2/2h)x1/(exp(hv/kT)-1)^(1/3)

5. Substitute in the given values for B, h, c, and k: v = ((10^-7)(3.0x10^8)^2/2(6.6x10^-34))x1/(exp((6.6x10^-34)v/(1.4x10^-23)(10^4))-1)^(1/3)

6. Simplify the equation: v = (9x10^-7/6.6x10^-34)x1/(exp(6.6x10^-30v)-1)^(1/3)

7. Use a calculator to solve for v: v = 1.5x10^15 Hz

I hope this helps. If you have any further questions or need clarification, please don't hesitate to ask.Scientist