It would no doubt be between 1845 - 1945.

In 1845 Faraday published his paper on the diamagnetic effect. This was the start of the electrical revolution that for the first time allowed us to connect the world by instant communication and also power our electrical motors for industry. At the same time Maxwell published his formulas on electromagnetism and realized light itself was one facet of this.

In 1869 Mendeleev published the Periodic Table of Elements. In the late 1800's work was truly beginning on the understanding of electrons and atoms by Thompson and Rutherford and many others. Marie Curie won a Nobel prize in 1903 for her work critical to understanding radiation. 1905 - 1915 Einstein published his papers on Relativity that changed physics forever. Edison invented the lightbulb and a practical way to record sound.

The quantum revolution (study of the sub-atomic structure) was in full swing in the 1920's -30's with the work of Bohr, Heisenberg, Schroedinger and countless others. The internal combustion engine made cars and even powered flight possible.

In the 1920's Flemming discovered antibiotics and for the first time in medical history a wound or simple ear infection didn't need to be a life or death issue. Infant mortality rates plummeted. In 1846 Morton began using modern Anesthesia. Until then surgury as we know it was not possible. It was 1940 that Turing gave us the Bombe - the world's first electro mechanical calculating machine, or a computer as well call them now.

Politically the map was always an ever changing mish-mash of borders continuously being redrawn, but in this span the world map settled in to a more permanent picture of how it looks today, more or less. This period also witnessed the height of the largest empire the world has ever seen, Victorian Britain.

We had BOTH world wars with perhaps 100 million people dead. This culminated with the invention of the atomic bomb in 1945.

So to sum up: We went from horse & buggy and not being able to send a message 10 miles let alone across the world - to a deep understanding of the atom all between 1845 and 1945. Pretty cool huh? ('cept the World War part.)

Your question is too vague to answer. What do you mean by change?

If you mean population change that would be after the industrial revolution. Or it could be in an era of major plague/war.

If you mean politically changed we could talk about Rome or post WW2.

If you mean philosphical change lets talk about the enlightenment.

Do you mean physically changed? That happens too slowly for a century except maybe post-industrial revolution and better nutrition.

Do you mean technological change? That would be early 19th - 20th century with the advent of electricity and the internal combustion engine.

If you can be more specific with your question it would give us a place to start.