# The blue mystery and the Raman effect

An elementary school level physics question: Why is the sky blue? You may answer that the sunlight gets scattered by the air-molecules and according to Rayleigh scattering theory, the blue light gets scattered the most (the scattering intensity proportional to $1/\lambda^4$, implying that it’s high for small wavelength $\lambda$ such as the blue light).

Now the immediate question comes: Why does sea look blue too?

Many school text-books explain in a simple and obvious way: Since the sky is blue, it’s reflection makes river or sea appear blue.

Though seems pretty convincing, the answer is incorrect and this week Tuesday Prof. Chandrabhas Narayan of JNCASR gave a beautiful lecture on Raman effect and how it becomes responsible for the blueness of sea.

He showed a few slides where all water resources don’t appear blue even though they are well-exposed under the sky. He explained in the following way. The Rayleigh scattering is an elastic scattering, where light just get deflected after confronting a molecule, but doesn’t change its wavelength. But there could be inelastic scattering processes due to vibrational modes of a molecules.

In an elastic scattering (Rayleigh one) an electron of a certain energy level inside an atom or a molecule absorbs energy from the incident photon and jumps to a higher energy state (called the virtual level) for a while and then emits the photon of the same energy (hence same wavelength too), and goes back to its original energy state.

However, in an inelastic scattering process, the electron can absorb the energy from a photon and then after reaching the virtual level it may decide to sit on one of its vibrational excited energy level by emitting a light with lower energy (hence higher wavelength). Such an emission line is known as the Stokes lines and the whole scattering process is known as the Raman Effect, discovered by C. V. Raman in 1928, who was a Palit Professor in Calcutta (His discovery helped him to get the Nobel prize very shortly, in 1930.).

The emission can go in the opposite direction as well (vibration level $\rightarrow$ virtual level $\rightarrow$ ground state of the atom/molecule ) and then the lines are called anti-Stokes lines.

Due to this Raman effect the water molecules in sea scatter the white sunlight to wavelengths that mostly fall in the blue regime of light spectra and hence sea appears blue.

Chandrabhas gave a long introduction (entertaining and answering several questions from the audience) of the Raman effect and its special importance in comparison to other spectroscopic measurements.

He said that it’s not necessary that sea or any water resource has to be blue in color (e.g. it can be turquoise) and the color depends on the depth of water as well.

He also mentioned that though Raman effect is very weak (out of $10^9$ photons, 1 photon participate in Raman scattering), a newly developed experimental probe called the Surface Enhance Raman Spectroscopy (SERS) can be very useful to characterize nanostructures and for biological fingerprint such as in DNAs and proteins. At the end Chandrabhas mentioned the controversies related to the real discoverers of this effect (e.g. Russians never liked to call it Raman effect, rather they preferred to say Mandelstam effect) and also the credit might have gone to Krishnan, one of Raman’s PhD student.

Prof. Chandrabhas’ talk can be found here.

Now may not be referred as a quiz question, but can you help the child to quench her curiosity?

# Celestial coincidence ! Great impact but no doomsday.

Guess everybody got the asteroid and meteorite news. Coincidentally both visited the earth almost at the same time (15 Feb, 2013). The asteroid, dubbed as 2012 DA14, met a record flyby (closest pass, which is about 17,000 miles or 27,000 km) to the earth and just went off without causing any harm to our planet.

On the other hand, the meteorite, which entered into Chelyabinsk, central Russia with a supersonic speed (about 33,000 mph), created shock waves, broke several window glasses and injured more than 1000 people.

Apart from the coincidence of the two celestial events, Russia has also become a common place of celestial devastation on earth. Though DA14 missed, it is believed that 1908 Tunguska event happened due to a collision of earth with an asteroid of a similar size (though some scientists argue that it was a comet actually).

Tunguska catastrophe: fallen trees, photograph by Leonid Kulik during his expedition in 1927 (courtesy: wikipedia).

It could be interesting to notice that the asteroid was discovered one year ago and its trajectory has been predicted beforehand, whereas the meteorite impact was unprecedented!

Now a quiz question:
What is the difference between a meteoroid/meteor and a meteorite?

# From physics to biology or biology to physics

Long back I posted about 3D printer and there I placed youtube videos showing that one can make real useful stuff such as a mechanical wrench or a bicycle suitable for riding. But so far 3D printing was limited to non-living physical objects. Now recently Dr Will Wenmiao Shu and his team members at Heriot-Watt University in Edinburgh, Scotland have successfully printed embryonic human stem cells (hESCs). Instead of usual inks for 3D printing, they have use the stem cells floating on a ‘bio ink’ for the printing. Replicating cells in this way carries future promises for organ replacement or regeneration.

Now another remarkable achievement, in a opposite sense (I mean, bio-stuff can be useful for physical non-bio application), has happened in the MIT lab, USA. Prof Timothy K Lu and his coleagues have found an innovative way to use DNA to produce logic gates that perform binary operations (often termed as Booolean Algbera). They have exploited a fancy property of the recombinase enzymes
on E. coli bacteria cells, that allow of prohibit (like ‘on/1’ and ‘off/0’ state of Boolean Algebra) gene transcription on certain conditions. A green fluorescent protein (GFP) has been used
as the output indicator (lighting of the GFP indicates an ‘on’ sate). The work has been published in this month’s Nature Biotechnology issue.

From the Nature Biotechnology paper by Siuti et al.

# Achieving the minus degree, but in a hotter way

Last year in a post, I discussed interpretations of a few quantities in our physical world, viz. energy, time, and mass. At the end I asked the readers to think about how we should understand negative temperature in absolute scale.

Recently in the ultra cold atoms in an optical lattice, such a negative temperature has been realized. The work has been published in the prestigious journal Science. Undoubtedly this is a remarkable achievement, but such a realization is not for the first time! E. M. Purcell (The NMR Guru) and his team found negative temeparature in the nuclear spin systems in LiF.

Instead of going deep into these experiments, let’s discuss how conceptually
we can think of temperature going to become negative.

Suppose we have a $N$ number of non-intercating spins in a magnetic field $B$.

At absolute zero temperature we expect the lowest energy state, i.e. when all the spins are aligned in the direction of the magnetic field (say, down) and the total energy will be $E=-N \mu B$, where $\mu$ is the dipole moment due to each spin. In this state (we call the ground state) all spins are aligned and hence ordered. So the entropy becomes zero. Another way to argue the same by can be done by looking at the number of possible configurations: $\Omega$. Since all spin alignment is unique, $\Omega=1$, hence entropy: $S =k_B\ln\Omega=\ln 1=0$ (The formula is popularly known as Boltzmann’s eq., where $k_B=1.38\times 10^{23}$ J/K is the Boltzmann constant).

Now suppose we provide an extra energy $\mu B$ so that one spin can flip from down to up. Now the total energy will be $E=(-N+1)\mu B$. Now since there is a disorder due to one flip, we start gaining a finite entropy. Following the alternative argument, we can see that now $\Omega=N$ since each among the $N$ spins equally qualify to flip. Thus the entropy becomes finite, i.e. $S= k_B \ln N \ge 0$. Now if more energy is provided then the entropy will start increasing, say, for two spins to flip, number of configurations will be $^N C _2=N(N-1)/2$. Thus entropy will be $S=k_B \ln N (N-1)/2$. Thus entropy will progess as $S= k_B \ln N (N-1)(N-2)/3$, and so on as we flip more and more spins. However, this progress will reach to a maximum when half of spin becomes remain down and the half gets flipped (up), i.e. $S_\text{max}=k_B \ln ^N C _{N/2}$. This maximum entropy value can be also thought as the middle block of a Pascal’s pyramid representing the middle ($N/2$-th) coefficient of a binomial expansion. Since the entropy becomes maximum at this point (i.e. an extremal point), differential change of entropy with energy becomes zero: $\frac{\partial S}{\partial E}=0$. And following the thermodynamic relation: $1/T=\frac{\partial S}{\partial E}$, we get $T=\infty$.

But trust me, infinity is not The End! So far we have added energy to the system and it became hotter and hotter. And we may always get tempted to say, the system becomes hottest at $T=\infty$. But surprisingly, if we add a little more energy to the system, we will find that entropy changes its mind: it starts decreasing now, as our configuration count moves away from the middle of the Pascal’s pyramid. Since entropy change becomes negative (implying decreasing trend), we start getting negative temperature, starting from a negative infinity, just after the positive (see the Fig. below). And now you may leave your skepticism and say that this negative $T$ regime is far hotter (In a patriarch pun, one can make an analogy: Black girls are far hotter than the white girls).

Sorry as I could not discuss about the recent optical lattice experiment as I’m always afraid that cold atoms are not my regular cup of tea. However, the basic idea (decreasing entropy) is the same, and I must confess that the Fig. that I have put above was stolen from the Science paper.