Diffraction Grating: Finding Wavelength with Given Angle and Slit Density

[seanmcgowan]

Homework Statement

Monochromatic light shines on the surface of a diffraction grating with 5.3x10^3 lines/cm. The first order maximum is observed at an angle of 17 (degrees). Find the wavelength.

a) 420nm c) 530nm
b) 520nm d) 550nm

Homework Equations

d(sin \Theta)=m\lambda

d= 5.3x10^lines/cm=5.3x10^3 lines/m

\Theta=17

m (the order maximum)= 1

The Attempt at a Solution

I rearranged the problem so it looked like this: \lambda=(d\Theta)/m

Since m=1, I dropped it and only worked with the numerator.

The distance between the slits is 1/53 metres so the full equation looks like this: (1/53)(sin17)= \lambda

(1/53)(.29)=\lambda
.0054716981=\lambda

Just by looking at this answer its easy to see its wrong, but why? I followed the equation, so what's up? Any help would be appreciated.

 

[Dadface]

d is not 1/5.3 it is 1/5.3 times 10 to the power of 6.

 

[seanmcgowan]

So my work was correct but i just needed that 10^6? thanks for the help