In grating spectrum, which spectral line in fifth order will overlap with fourth orderline of 5890 Å.

To solve this problem, we need to use the formula for diffraction grating:

dsin(θ) = mλ

where:

• d is the distance between the slits in the grating,
• θ is the angle of diffraction,
• m is the order of the spectrum,
• λ is the wavelength of the light.

We are looking for the wavelength (λ) that will cause the 5th order spectrum to overlap with the 4th order spectrum of 5890 Å.

So, we set up the equation as follows:

dsin(θ) = 5λ (equation 1)

and

dsin(θ) = 45890 Å (equation 2)

Since the two spectra are overlapping, the angles of diffraction (θ) and the distance between the slits (d) are the same for both equations. Therefore, we can set the two equations equal to each other and solve for λ:

5λ = 45890 Å

Solving for λ gives:

λ = (4*5890 Å) / 5 = 4712 Å

So, the 5th order spectral line that will overlap with the 4th order line of 5890 Å is 4712 Å.