Physics, 21.12.2020 18:10 haileysolis5

A diffraction grating with 68 slits per cm is used to measure the wavelengths emitted by hydrogen gas. A. At what angles in the fourth-order spectrum would you expect to find the two violet lines of wavelength 434 nm and of wavelength 410 nm?
B. What are the angles if the grating has 12,800 slits per cm?

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Answer from: bxbysoso

$\theta _1 =0.687 ^o$

$\theta _2 =0.630 ^o$

Generally given that the domain arcsine function is between -1 and 1 then the arcsine of 2.22 will not be valid

Generally given that the domain arcsine function is between -1 and 1 then the arcsine of 2.1 will not be valid

Explanation:

From the question we are told that

The slit grating is $N = 68 \ slits / cm = 6800 \ slits / m$

The order of spectrum is n = 4

Generally the width of the slit is mathematically represented as

$a = \frac{1}{ 6800}$

=> $a = 0.000147 \ m$

Generally the condition for constructive interference is

$asin\theta = n * \lambda$

Now for the first wavelength the angle is evaluated as

$\theta _1 = sin ^{-1} [ \frac{n \lambda_1 }{a} ]$

=> $\theta _1 = sin ^{-1} [ \frac{4* 434 *10^{-9} }{ 0.000147 } ]$

=> $\theta _1 =0.687 ^o$

Now for the second wavelength the angle is evaluated as

$\theta _2 = sin ^{-1} [ \frac{n \lambda_2 }{a} ]$

=> $\theta _2 = sin ^{-1} [ \frac{4* 410 *10^{-9} }{ 0.000147 } ]$

=> $\theta _2 =0.630 ^o$

Gnerally if grating is $N = 12800 \ slits per cm = 1280000 \ slits / m$

Generally the width of the slit is mathematically represented as

$a = \frac{1}{ 1280000}$

=> $a = 7.813 *10^{-7} \ m$

Generally the condition for constructive interference is

$asin\theta = n * \lambda$

Now for the first wavelength the angle is evaluated as

$\theta _1 = sin ^{-1} [ \frac{n \lambda_1 }{a} ]$

$\theta _1 = sin ^{-1} [ \frac{4* 434 *10^{-9} }{ 7.813*10^{-7} } ]$

=> $\theta _1 = sin ^{-1} [ 2.22]$

Generally given that the domain arcsine function is between -1 and 1 then the arcsine of 2.22 will not be valid

=> $\theta _1 =0.687 ^o$

Now for the second wavelength the angle is evaluated as

$\theta _2 = sin ^{-1} [ \frac{n \lambda_2 }{a} ]$

=> $\theta _2 = sin ^{-1} [ \frac{4* 410 *10^{-9} }{ 7.813*10^{-7} } ]$

=> $\theta _2 = sin ^{-1} [2.1 ]$

Generally given that the domain arcsine function is between -1 and 1 then the arcsine of 2.22 will not be valid

Answer from: Quest

i think the answer would be reserve.

Answer from: Quest

There is no graph to look at on here, but i shall explain them to you. a line graph is just in its title it’s a graph with a line running through the dots to show an increase or decrease. a bar graph is used to show how much or how little something is so a comparison. a scatter plot is used to graph points to tell the data. and i don’t know what a histogram is.

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