Question $3,$ chap $141,$ sect $4.$

part $1$ of $3,10$ points

A transmission diffraction grating with $575$ lines $\frac{?}{mm}$ is used to study the line spectrum of the light produced by a hydrogen discharge tube with setup shown below.

The grating is $1\mathrm{.}1$ m from the source $($a hole at the center of the meter stick$).$ An observer sees the first$-$order red line at a distance $y_{\text{r}\text{e}\text{d}}=0\mathrm{.}259792$ m from the hole.

The speed of light is $2\mathrm{.}998{10}^8\frac{m}{s}$ and the Planck's constant is $6\mathrm{.}626{10}^{-34}J*s.$

Calculate the wavelength of the red line in the hydrogen spectrum.

Answer in units of $m.$

Question $4,$ chap $141,$ sect $4.$

part $2$ of $3$ points

According to the Bohr model, the energy levels of the hydrogen atom are given by $E_n=-\frac{13\mathrm{.}6eV}{n^2},$ where $n$ is an integer identifying the levels. The red line in our question is a transition to a final level with $n=2.$

Use the Bohr model to determine the value of $n$ for the initial level of the transition.

Question $5,$ chap $141,$ sect $4.$

part $3$ of $3$

$10$ points

If a diffraction grating with $675$ lines$/$mm were used instead of one with $575$ lines $\frac{?}{mm},$ determine the location of the first$-$order red line.

Answer in units of $m.$