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Why are the molecules which are superimposable on their mirror images optically inactive? For example 1-bromo-2-methylpropane.

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    $\begingroup$ Why, that's simple. Imagine an experimental setup in which one such compound rotates light clockwise. Now imagine another setup, where everything (all the way down to molecules) is the mirror image of the first setup. Being a mirror image, it would rotate light counterclockwise. But wait, the molecules are the same! How can they know which way to rotate the light? They can't and don't. $\endgroup$ – Ivan Neretin Dec 29 '18 at 11:05
  • $\begingroup$ Thanks a lot ivan...but could you explain it in a more scientific way just in case someone asks about this wrt symmetry and chirality $\endgroup$ – Simran girdhar batra Dec 29 '18 at 11:14
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    $\begingroup$ There is no reason to look for a mirror image. The key is intrinsic and is symmetry. Look here chemistry.stackexchange.com/questions/83990/… $\endgroup$ – Alchimista Dec 29 '18 at 11:27
  • $\begingroup$ In other words the polarization is unaffected even by a single molecule - when the latter has symmetry. $\endgroup$ – Alchimista Dec 29 '18 at 11:58
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Individual molecules will react with incoming photons depending on their orientation in space. So–at an individual molecule level–light can be rotated in polarity if the molecule has a particular structure. But in the bulk, the molecules will be randomly oriented and the effect of any single interaction will be cancelled out by other, opposite, interactions.

The exceptions to this are crystals where the overall structure is chiral so the orientation of the molecules or components of the crystal don't allow a random mix of orientations so there is a net effect on the polarisation of the light (quartz or calcite are examples).

The other exception is where molecules are chiral. If the image of the molecule in a mirror is different to the original molecule then no amount of randomness in how the molecule is oriented in space will cancel out the individual interactions of polarised light with the molecules and there will be optical activity.

Molecules which are superimposable on their mirror images don't have this property because rotating and translating them in space will provide a random mix of orientations that always cancels out to nothing when interacting with polarised light. Randomly translating or rotating a chiral molecule cannot achieve this as there is no way to create an opposite orientation in space that is the equivalent of a mirror image just by using rotations and translations.

This is basically a geometry issue: molecules that are the same as their mirror image can be rotated and translated to any possible orientation and so show no net interaction with light in the bulk on average whatever the individual molecules does. Molecules where their mirror image isn't the same don't average out to a zero interaction however you rotate or translate them.

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