Answer:
n = 3
Solution:
Since, the slit used is same and hence slit distance 'x' will also be same.
Also, the wavelengths coincide, [tex]\theta [/tex] will also be same.
Using Bragg's eqn for both the wavelengths:
[tex]xsin\theta = n\lambda[/tex]
[tex]xsin\theta = n\times 680.0\times 10^{- 9}[/tex] (1)
[tex]xsin\theta = (n + 1)\lambda[/tex]
[tex]xsin\theta = (n + 1)\times 510.0\times 10^{- 9}[/tex] (2)
equate eqn (1) and (2):
[tex] n\times 680.0\times 10^{- 9} = (n + 1)\times 510.0\times 10^{- 9}[/tex]
[tex]n = \frac{510.0\times 10^{- 9}}{680.0\times 10^{- 9} - 510.0\times 10^{- 9}}[/tex]
n = 3
