[Ricky2015]

State whether true or false :

$S_1$ :  When an electron makes transition form higher orbit to lower orbit it's kinetic energy increases.

$S_2$ :  When an electron makes a transition from lower energy to higher energy state its potential energy increases.

My Answer :

Since , negative sign of energy doesnt matter in comparing which is large or small . Thus the answer should be True , False .

But the book says that both of them are true .

My doubt : Should enegative sign be strictly considered when comparing energies ?

[clinz63]

The greater the distance between two opposite charged particles, the greater the electrostatic attraction. Ergo, greater potential energy.

[mjc123]

My doubt : Should enegative sign be strictly considered when comparing energies ?

Yes. Using the convention that the potential energy is zero at infinite separation, all bound states have negative potential energy; in the higher state it is less negative (i.e. greater) than in the lower state. But this is just a convention. There is no absolute zero of energy. We could choose to say the potential energy of the lowest possible state of the electron in the atom is zero, and measure all the other states relative to that, in which case they would be positive.
Think about it. If you go from -10 to -5°C, is the temperature increasing or decreasing. What about 14 to 23°F? or 263 to 268K?

[Enthalpy]

[...] negative sign of energy doesnt matter in comparing which is large or small[...]

Energy is a signed quantity. You compare two energies as such.

[Borek]

The greater the distance between two opposite charged particles, the greater the electrostatic attraction.

Quite the opposite, attraction changes as [itex]\frac 1 {r^2}[/itex].

[clinz63]

Yes. My bad. There is less attraction but there is greater potential energy. Got carried away by the greater potential energy. 

[Ricky2015]

Yes. My bad. There is less attraction but there is greater potential energy. Got carried away by the greater potential energy. 

So we conclude that
since

potential energy = - k Ze^2/r

=> the more the r , the less negative is PE , so PE increases as we move up to higher levels .

[mikasaur]

So we conclude that
since

potential energy = - k Ze^2/r

=> the more the r , the less negative is PE , so PE increases as we move up to higher levels .

Yes. [itex]-\frac{1}{2}<-\frac{1}{4}[/itex]. Mathematically that's how you can think of it. Conceptually it's similar to gravitational potential energy but the signs are reversed.

For gravity you can say that the floor is where items have zero potential energy. And as you move an item off the floor it gains potential energy -- a positive number. When you drop an object it changes its potential energy into kinetic. But what happens if you dig a hole in the floor? Is the bottom of the hole now 0 PE? Or is it negative? It doesn't really matter because it's all arbitrary. What remains the same is the change in energy.