Question

Atomic Spectroscopy

1. Whenever you look at an element undergoing fluorescence, why do you see multiple colors in a line spectrum, but only a single color with your un-aided eyes?
2. Calculate energy associated with the four major energy transitions in the hydrogen atom. Assume the final energy level is 2 for each.

Answer 1

1.

We know that there are multiple lines of different wavelengths (i.e different colors) in a line spectrum. When we look with our unaided eyes, the different color lights combine and our brain interprets them as a single color, for example, a green and red line near each other will be perceived as yellow light by our brain.

But when we look at the line spectrum with a spectroscope, the diffraction grating (it acts like a prism) in the spectroscope separates the colors substantially so that they are away from each other and our brain is able to differentiate them.

2.

For hydrogen atom, the energy of the nth level is given by the following equation:

En = -2.18 x 10-18J

Where n is the principal quantum number deciding the energy level.

The first four major transitions from higher levels to energy level with n=2 are

n = 3 →n= 2

n=4 →n=2

n = 5 →n=2

n=6 →n=2

Hence, the energy of the four major transition can be calculated by subtracting the energy of the initial state from the final state.

Hence,

For

n = 3 →n= 2

AE372 = E3 – E2 = -2.18 x 10-18 AE3-2 = 3.03 x 10-19 J

Similarly, for

n=4 →n=2

ΔΕ4-2 = E4 - E2 = -2.18x 10-18 (42- = ΔΕ_2 = 4.09 x 10-19 )

Similarly, for

n = 5 →n=2

AE52 = Es – E2 = -2.18 x 10-18 AE52 = 4.58 x 10-19 J

Similarly, for

n=6 →n=2

AE62 = E6 – E2 = -2.18 x 10-18 62 AE6–2 = 4.85 x 10-19 J

Hence, the first four energy of transition to n=2 level are
3.03 < 10-19 J, 4.09 x 10-19 J, 4.58 x 10-19 , 4.85 10-19 J
.