What technology do you think is responsible for giving us these bountiful appliance as well as your handheld gadgets?

Electronics (mainly), discovery of quantum mechanics, transistors, element properties, etc.

Explanation:

Great question. I think that it's widely agreed upon that the existence of handheld gadgets, as well as most electronics such as these, came from the advent of quantum mechanics (QM). Quantum mechanics allowed us to look at the behavior of electrons, as they are different from everyday objects. You can think of QM at the interface of chemistry and physics. Quantum mechanics is important, considering it predicts how electrons have to flow through your phone. This was especially helpful in determining their behavior regarding solid materials like the ones that make up your phone. Also, there are several materials that go into a phone, among these certain elements, such as silicon (a semiconductor) and copper/silver, which are great at conducting electrons. Eventually we started using things called transistors, which can amplify and switch electronic signals when needed. These can thought to be a direct product of QM. There are also all kinds of diodes and things that can emit light, among other things.

Also, you have to get the electricity from somewhere, and that can come from a controlled chemical reaction that you can charge right in your phone! That is basically what a battery does, it converts chemical energy (using chemical reactions) into electrical energy that powers your phone. So in short, electronics, chemistry of materials (governed by physics) and especially understanding of how electrons work with tiny transistors in your phone come together to even show you this answer. Wow.

ingenuity says that the answer is 2.7 m.