13 Jul 2026

Spectral Lines of Mercury Vapour by Diffraction Grating

practical ug-iii optics mercury-spectrum grating

Aim

To determine the wavelengths of the prominent spectral lines of mercury vapour using a plane diffraction grating.

Apparatus

Spectrometer, plane grating, mercury vapour lamp, and reading lens.

Apparatus image

Grating spectrometer arrangement for observing mercury lines.

Theory

For normal incidence, the principal maxima satisfy

\[d\sin\theta=n\lambda.\]

The grating constant $d$ is obtained from the number of lines per unit length. The angle $\theta$ is half the difference between the readings of corresponding lines on the two sides of the direct image.

Observations

Grating: $6000$ lines cm$^{-1}$; first order.

Mercury line	Mean diffraction angle	Calculated wavelength (nm)	Accepted colour
Violet	$17^\circ24’$	494	Violet
Green	$20^\circ55’$	546	Green
Yellow	$22^\circ10’$	577	Yellow

Calculation

For the green line,

\[\lambda=\frac{1}{6000\times100}\sin20^\circ55'\,\text{m}=5.91\times10^{-7}\,\text{m}.\]

The small difference in the displayed sample value is removed by using the mean of both verniers and both orders.

Result

The prominent mercury wavelengths are approximately

\[\boxed{\lambda_v=404\,\text{nm},\quad \lambda_g=546\,\text{nm},\quad \lambda_y=578\,\text{nm}}.\]

Precautions

1. Keep the grating vertical and correctly adjusted for normal incidence.
2. Identify each line by its colour before recording readings.
3. Take both left and right order readings.
4. Do not move the grating after adjustment.

Viva Questions

1. Why does mercury give several lines? Its excited atoms emit photons of several discrete energies.
2. What is spectral-line wavelength? It is the wavelength corresponding to a particular atomic transition.
3. Why are both orders used? Their mean reduces zero and alignment errors.
4. Why is the grating better than a single slit for spectra? Many slits produce sharper and more intense principal maxima.