Question

Light of wavelength 656 nm and 410 nm emitted from a hot gas of hydrogen atoms strikes a grating with 5300 lines per centimeter. a) Determine the angular deflection of both wavelengths in the 1st and 2nd order.

Answer 1

`20.32^(\circ)` and
`44.08^(\circ)`

`12.56^(\circ)` and
`25.77^(\circ)`

Step-by-step explanation:

`\lambda` = Wavelength

`\theta` = Angle

m = Order

Distance between grating is given by

`d=(1)/(5300)\\\Rightarrow d=0.0001886\ \text{cm}`

`\lambda=656\ \text{nm}`

We have the relation

`d\sin\theta=m\lambda\\\Rightarrow \theta=\sin^(-1)(m\lambda)/(d)`

m = 1

`\theta=\sin^(-1)(1* 656* 10^(-9))/(0.0001886* 10^(-2))\\\Rightarrow \theta=20.35^(\circ)`

m = 2

`\theta=\sin^(-1)(2* 656* 10^(-9))/(0.0001886* 10^(-2))\\\Rightarrow \theta=44.08^(\circ)`

The first and second order angular deflection is
`20.32^(\circ)` and
`44.08^(\circ)`

`\lambda=410\ \text{nm}`

m = 1

`\theta=\sin^(-1)(1* 410* 10^(-9))/(0.0001886* 10^(-2))\\\Rightarrow \theta=12.56^(\circ)`

m = 2

`\theta=\sin^(-1)(2* 410* 10^(-9))/(0.0001886* 10^(-2))\\\Rightarrow \theta=25.77^(\circ)`

The first and second order angular deflection is
`12.56^(\circ)` and
`25.77^(\circ)`.