# In a grating spectrum, which spectral line in fourth order will overlap with third order line of 5461 A^0

In a grating spectrum, which spectral line in fourth order will overlap with third order line of $5461{A}^{0}$
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Kaiden Weeks
Given
The wavelength of a spectral line in third-order is ${\lambda }_{3}=5461{A}^{0}$
The integer of the third order is ${n}_{3}=3.$
The integer of the fourth-order is ${n}_{4}=4.$
If the grating spectrum is the same for both the orders then,
$n\lambda =\text{constant}\phantom{\rule{0ex}{0ex}}{n}_{3}{\lambda }_{3}={n}_{4}{\lambda }_{4}$
Here, ${\lambda }_{4}$ is the wavelength of a spectral line in fourth-order.
Substitute the known values.
$3×5461{A}^{0}=4×{\lambda }_{4}\phantom{\rule{0ex}{0ex}}{\lambda }_{4}=\frac{3×5461{A}^{0}}{4}\phantom{\rule{0ex}{0ex}}=4095.75{A}^{0}$
Thus, in the grating spectrum, the wavelength of the spectral line of fourth-order is $4095.75{A}^{0}$