Which electron transition represents a gain of energy?
a. from 2nd to 3rd shell
b. from 2nd to 1st shell
c. from 3rd to 2nd shell
d. from 3rd to 1st shell

The correct answer is (A) from 2nd to 3rd shell.

The explanation :

when a gain of energy is the shift of the electrons from a shell of low energy to the shell of high energy

and we have here 2nd shell is the shell of low energy, and 3rd shell is the shell of high energy.

∴ (A) from 2nd to 3rd shell is the correct answer.

it can be observed without changing the identity of the object.

it depends on what substance you're talking about as well as many other factors. in quantum mechanics, the observation of particles affects the observers ability to measure certain properties. for example: you can know the velocity of a particle, but you can't know it's position; or you can know it's position, but not it's velocity. it's like trying to find out where a grain of sand is by throwing other grains of sand at it. once you find out where it is, it's been moved. it's also like trying to find an answer to the question of whether or not a tree falling in a forest makes a sound if nobody is there to hear it. paradoxically, the only way to find out is to be there and hear it.